Sorption kinetics of diuron on volcanic ash derived soils.

PubMed

Cáceres-Jensen, Lizethly; Rodríguez-Becerra, Jorge; Parra-Rivero, Joselyn; Escudey, Mauricio; Barrientos, Lorena; Castro-Castillo, Vicente

2013-10-15

Diuron sorption kinetic was studied in Andisols, Inceptisol and Ultisols soils in view of their distinctive physical and chemical properties: acidic pH and variable surface charge. Two types of kinetic models were used to fit the experimental dates: those that allow to establish principal kinetic parameters and modeling of sorption process (pseudo-first-order, pseudo-second-order), and some ones frequently used to describe solute transport mechanisms of organic compounds on different sorbents intended for remediation purposes (Elovich equation, intraparticle diffusion, Boyd, and two-site nonequilibrium models). The best fit was obtained with the pseudo-second-order model. The rate constant and the initial rate constant values obtained through this model demonstrated the behavior of Diuron in each soil, in Andisols were observed the highest values for both parameters. The application of the models to describe solute transport mechanisms allowed establishing that in all soils the mass transfer controls the sorption kinetic across the boundary layer and intraparticle diffusion into macropores and micropores. The slowest sorption rate was observed on Ultisols, behavior which must be taken into account when the leaching potential of Diuron is considered. Copyright © 2013 Elsevier B.V. All rights reserved.

The effect of metal (hydr)oxide nano-enabling on intraparticle mass transport of organic contaminants in hybrid granular activated carbon.

PubMed

Garcia, Jose; Markovski, Jasmina; McKay Gifford, J; Apul, Onur; Hristovski, Kiril D

2017-05-15

The overarching goal of this study was to ascertain the changes in intraparticle mass transport rates for organic contaminants resulting from nano-enabled hybridization of commercially available granular activated carbon (GAC). Three different nano-enabled hybrid media were fabricated by in-situ synthesizing titanium dioxide nanoparticles inside the pores of GAC sorbent, characterized, and evaluated for removal of two model organic contaminants under realistic conditions to obtain the intraparticle mass transport (pore and surface diffusion) coefficients. The results validated the two hypotheses that: (H1) the pore diffusion rates of organic contaminants linearly decrease with decrease in cumulative pore volume caused by increase in metal (hydr)oxide nanoparticle content inside the pores of the hybrid GAC sorbent; and (H2) introduction of metal (hydr)oxide nanoparticles initially increases surface diffusivity, but additional loading causes its decrease as the increase in metal (hydr)oxide nanoparticles content continues to reduce the porosity of the GAC sorbent. Nano-enabled hybridization of commercially available GAC with metal (hydr)oxides has the potential to significantly increase the intraparticle mass transport limitations for organic contaminants. Introduction of metal (hydr)oxide nanoparticles inside the pores of a pristine sorbent causes the pore diffusion rates of organic contaminants to decrease as the cumulative pore volume is reduced. In contrast, the introduction of limited amounts of metal (hydr)oxide nanoparticles appears to facilitate the surface diffusion rates of these contaminants. Copyright © 2017 Elsevier B.V. All rights reserved.

Synthesis of hierarchical Ni(OH)(2) and NiO nanosheets and their adsorption kinetics and isotherms to Congo red in water.

PubMed

Cheng, Bei; Le, Yao; Cai, Weiquan; Yu, Jiaguo

2011-01-30

Ni(OH)(2) and NiO nanosheets with hierarchical porous structures were synthesized by a simple chemical precipitation method using nickel chloride as precursors and urea as precipitating agent. The as-prepared samples were characterized by X-ray diffraction, scanning electron microscopy and nitrogen adsorption-desorption isotherms. Adsorption of Congo red (CR) onto the as-prepared samples from aqueous solutions was investigated and discussed. The pore structure analyses indicate that Ni(OH)(2) and NiO nanosheets are composed of at least three levels of hierarchical porous organization: small mesopores (ca. 3-5 nm), large mesopores (ca. 10-50 nm) and macropores (100-500 nm). The equilibrium adsorption data of CR on the as-prepared samples were analyzed by Langmuir and Freundlich models, suggesting that the Langmuir model provides the better correlation of the experimental data. The adsorption capacities for removal of CR was determined using the Langmuir equation and found to be 82.9, 151.7 and 39.7 mg/g for Ni(OH)(2) nanosheets, NiO nanosheets and NiO nanoparticles, respectively. Adsorption data were modeled using the pseudo-first-order, pseudo-second-order and intra-particle diffusion kinetics equations. The results indicate that pseudo-second-order kinetic equation and intra-particle diffusion model can better describe the adsorption kinetics. The as-prepared Ni(OH)(2) and NiO nanosheets are found to be effective adsorbents for the removal of Congo red pollutant from wastewater as a result of their unique hierarchical porous structures and high specific surface areas. Copyright © 2010 Elsevier B.V. All rights reserved.

Preparation of char from lotus seed biomass and the exploration of its dye removal capacity through batch and column adsorption studies.

PubMed

Nethaji, S; Sivasamy, A; Kumar, R Vimal; Mandal, A B

2013-06-01

Char was obtained from lotus seed biomass by a simple single-step acid treatment process. It was used as an adsorbent for the removal of malachite green dye (MG) from simulated dye bath effluent. The adsorbent was characterized for its surface morphology, surface functionalities, and zero point charge. Batch studies were carried out by varying the parameters such as initial aqueous pH, adsorbent dosage, adsorbent particle size, and initial adsorbate concentration. Langmuir and Freundlich isotherms were used to test the isotherm data and the Freundlich isotherm best fitted the data. Thermodynamic studies were carried out and the thermodynamic parameters such as ∆G, ∆H, and ∆S were evaluated. Adsorption kinetics was carried out and the data were tested with pseudofirst-order model, pseudosecond-order model, and intraparticle diffusion model. Adsorption of MG was not solely by intraparticle diffusion but film diffusion also played a major role. Continuous column experiments were also conducted using microcolumn and the spent adsorbent was regenerated using ethanol and was repeatedly used for three cycles in the column to determine the reusability of the regenerated adsorbent. The column data were modeled with the modeling equations such as Adam-Bohart model, Bed Depth Service Time (BDST) model, and Yoon-Nelson model for all the three cycles.

Graphene oxide coated with porous iron oxide ribbons for 2, 4-Dichlorophenoxyacetic acid (2,4-D) removal.

PubMed

Nethaji, S; Sivasamy, A

2017-04-01

Graphene oxide (GO) was prepared from commercially available graphite powder. Porous iron oxide ribbons were grown on the surface of GO by solvothermal process. The prepared GO-Fe 3 O 4 nanocomposites are characterized by FT-IR, XRD, VSM, SEM, TEM, Raman spectroscopy, surface functionality and zero point charge studies. The morphology of the iron oxide ribbons grown on GO is demonstrated with TEM at various magnifications. The presence of magnetite nanoparticles is evident from XRD peaks and the magnetization value is found to be 37.28emu/g. The ratio of intensity of D-peak to G-peak from Raman spectrum is 0.995. The synthesized Graphene oxide-Fe 3 O 4 nanocomposites (GO-Fe 3 O 4 ) were explored for its surface adsorptive properties by using a model organic compound, 2,4-Dichlorophenoxy acetic acid (2,4-D) from aqueous solution. Batch adsorption studies were performed and the equilibrium data are modelled with Langmuir, Freundlich and Temkin isotherms. The maximum monolayer capacity from Langmuir isotherm is 67.26mg/g. Kinetic studies were also carried out and the studied adsorption process followed pseudo second-order rate equation. Mechanism of the adsorption process is studied by fitting the data with intraparticle diffusion model and Boyd plot. The studied adsorption process is both by film diffusion and intraparticle diffusion. Copyright © 2017 Elsevier Inc. All rights reserved.

Comparison between the intra-particle diffusivity in the hydrophilic interaction chromatography and reversed phase liquid chromatography modes. Impact on the column efficiency.

PubMed

Gritti, Fabrice; Guiochon, Georges

2013-07-05

The effective diffusion coefficients of five low molecular weigh compounds (naphthalene, uracil, uridine, adenosine, and cytosine) were measured at room temperature in a 4.6mm×100mm column packed with 3.5μm XBridge HILIC particles. The mobile phase was an acetonitrile-water mixture (92.5/7.5, v/v) containing 10mM ammonium acetate and 0.02% acetic acid. Using a physically reliable model of effective diffusion in binary composite media (Torquato's model), accurate estimates of the intra-particle diffusivities in the HILIC particles were obtained as a function of the retention of these analytes. The HILIC diffusion coefficients were compared to those previously obtained for endcapped RPLC-C18 particles (5.0μm Gemini-C18). The experimental results confirm that adsorption sites are not localized in RPLC whereas they are so in the HILIC mode. In contrast to RPLC columns, HILIC columns provide longitudinal diffusion B/u terms that increase very little with increasing retention factors. This confirms the absence of surface diffusion in HILIC. The impact of intra-particle diffusivity on the column efficiency was projected in HILIC and RPLC on the basis of the measured intra-particle diffusivities and on the well established theory of band broadening in particulate columns. Accordingly, RPLC columns generate short-range eddy dispersion and solid-liquid mass transfer resistance Cu terms that increase less than do HILIC column with increasing retention factors. The HETP contribution caused by the trans-column structure heterogeneity is smaller in the HILIC than in the RPLC modes because the transverse excursion length is smaller in HILIC. Even though the overall column efficiencies are comparable in HILIC and RPLC, this study shows that the individual mass transfer phenomena are inherently different in the HILIC and the RPLC retention modes. Copyright © 2013 Elsevier B.V. All rights reserved.

Adsorption kinetics of NO on ordered mesoporous carbon (OMC) and cerium-containing OMC (Ce-OMC)

NASA Astrophysics Data System (ADS)

Chen, Jinghuan; Cao, Feifei; Chen, Songze; Ni, Mingjiang; Gao, Xiang; Cen, Kefa

2014-10-01

Ordered mesoporous carbon (OMC) and cerium-containing OMC (Ce-OMC) were prepared using evaporation-induced self-assembly (EISA) method and used to adsorb NO. N2 sorption, X-ray diffraction (XRD) and transmission electron microscopy (TEM) were used to confirm their structures. The results showed that the ordered and uniform structures were successfully synthesized and with the introduction of cerium pore properties were not significantly changed. The NO adsorption capacity of OMC was two times larger than that of activated carbon (AC). With the introduction of cerium both the adsorption capacity and the adsorption rate were improved. The effects of residence time and oxygen concentration on NO adsorption were also investigated. Oxygen played an important role in the NO adsorption (especially in the form of chemisorption) and residence time had small influence on the NO adsorption capacity. The NO adsorption kinetics was analyzed using pseudo-first-order, pseudo-second-order, Elovich equation and intraparticle diffusion models. The results indicated that the NO adsorption process can be divided into rapid adsorption period, slow adsorption period, and equilibrium adsorption period. The pseudo-second-order model was the most suitable model for NO adsorption on OMC and Ce-OMC. The rate controlling step was the intraparticle diffusion together with the adsorption reaction.

Removal of dieldrin from aqueous solution by a novel triolein-embedded composite adsorbent.

PubMed

Ru, Jia; Liu, Huijuan; Qu, Jiuhui; Wang, Aimin; Dai, Ruihua

2007-03-06

In this study, a novel triolein-embedded activated carbon composite adsorbent (CA-T) was prepared and applied for the adsorption and removal of dieldrin from aqueous systems. Experiments were carried out to investigate the adsorption behavior of dieldrin on CA-T, including adsorption isotherms, adsorption kinetics, the influence of initial concentration, temperature, shaking speed, pH and the addition of humic acid (HA) on adsorption. The adsorption isotherms accorded with Freundlich equation. Three kinetics models, including pseudo-first-order, pseudo-second-order and intraparticle diffusion models, were used to fit the experimental data. By comparing the correlation coefficients, it was found that both pseudo-second-order and intraparticle diffusion models were used to well describe the adsorption of dieldrin on CA-T. The addition of HA had little effect on dieldrin adsorption by CA-T. Results indicated that CA-T appeared to be a promising adsorbent for removing lipophilic dieldrin in trace amount, which was advantageous over pure granular activated carbon (GAC). The adsorption rate increased with increasing shaking speed, initial concentration and temperature, and remained almost unchanged in the pH range of 4-8. Thermodynamic calculations indicated that the adsorption reaction was spontaneous with a high affinity and the adsorption was an endothermic reaction.

Optimization of the combined ultrasonic assisted/adsorption method for the removal of malachite green by gold nanoparticles loaded on activated carbon: experimental design.

PubMed

Roosta, M; Ghaedi, M; Shokri, N; Daneshfar, A; Sahraei, R; Asghari, A

2014-01-24

The present study was aimed to experimental design optimization applied to removal of malachite green (MG) from aqueous solution by ultrasound-assisted removal onto the gold nanoparticles loaded on activated carbon (Au-NP-AC). This nanomaterial was characterized using different techniques such as FESEM, TEM, BET, and UV-vis measurements. The effects of variables such as pH, initial dye concentration, adsorbent dosage (g), temperature and sonication time on MG removal were studied using central composite design (CCD) and the optimum experimental conditions were found with desirability function (DF) combined response surface methodology (RSM). Fitting the experimental equilibrium data to various isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin-Radushkevich models show the suitability and applicability of the Langmuir model. Kinetic models such as pseudo -first order, pseudo-second order, Elovich and intraparticle diffusion models applicability was tested for experimental data and the second-order equation and intraparticle diffusion models control the kinetic of the adsorption process. The small amount of proposed adsorbent (0.015 g) is applicable for successful removal of MG (RE>99%) in short time (4.4 min) with high adsorption capacity (140-172 mg g(-1)). Copyright © 2013. Published by Elsevier B.V.

Intraparticle diffusion limitations in the hydrogenation of monounsaturated edible oils and their fatty acid methyl esters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jonker, G.H.; Veldsink, J.W.; Beenackers, A.A.C.M.

1998-12-01

Intraparticle diffusion limitation in the hydrogenation and isomerization of fatty acid methyl esters (FAMEs) and edible oils (triacylglycerol, TAG) in porous nickel catalyst was investigated both under reactive and under inert conditions. Under reactive conditions, the diffusion coefficients were determined from the best fits of the model simulations applying the intrinsic reacting kinetics of monounsaturated FAME hydrogenation to experiments under diffusion limited conditions. Due to the absence of reaction (hydrogenation of double bonds), the obtained effective H{sub z} diffusion coefficient (D{sub e}) with the HPLC technique is volume averaged and thereby determined by the larger intercrystalline pores (<30% of themore » total pore volume) only. Moreover, D{sub e} measured under reaction conditions reflected the influence of the micropores, resulting in a 10-fold lower value.« less

Optimization of methylene blue using Ca(2+) and Zn(2+) bio-polymer hydrogel beads: A comparative study.

PubMed

Kumar, M; Tamilarasan, R; Arthanareeswaran, G; Ismail, A F

2015-11-01

Recently noted that the methylene blue cause severe central nervous system toxicity. It is essential to optimize the methylene blue from aqueous environment. In this study, a comparison of an optimization of methylene blue was investigated by using modified Ca(2+) and Zn(2+) bio-polymer hydrogel beads. A batch mode study was conducted using various parameters like time, dye concentration, bio-polymer dose, pH and process temperature. The isotherms, kinetics, diffusion and thermodynamic studies were performed for feasibility of the optimization process. Freundlich and Langmuir isotherm equations were used for the prediction of isotherm parameters and correlated with dimensionless separation factor (RL). Pseudo-first order and pseudo-second order Lagegren's kinetic equations were used for the correlation of kinetic parameters. Intraparticle diffusion model was employed for diffusion of the optimization process. The Fourier Transform Infrared Spectroscopy (FTIR) shows different absorbent peaks of Ca(2+) and Zn(2+) beads and the morphology of the bio-polymer material analyzed with Scanning Electron Microscope (SEM). The TG & DTA studies show that good thermal stability with less humidity without production of any non-degraded products. Copyright © 2015 Elsevier Inc. All rights reserved.

An adsorption diffusion model for removal of para-chlorophenol by activated carbon derived from bituminous coal.

PubMed

Sze, M F F; McKay, G

2010-05-01

Batch adsorption experiments were carried out to study the adsorptive removal and diffusion mechanism of para-chlorophenol (p-CP) onto Calgon Filtrasorb 400 (F400) activated carbon. The external mass transfer resistance is negligible in the adsorption process carried out under different conditions in batch operation. Intraparticle diffusion model plots were used to correlate the batch p-CP adsorption data; three distinct linear sections were obtained for every batch operation. The textural properties of F400 activated carbon showed that it has a large portion of supermicropores, which is comparable to the size of the p-CP molecules. Due to the stronger interactions between p-CP molecules and F400 micropores, p-CP molecules predominantly diffused and occupied active sites in micropore region by hopping mechanism, and eventually followed by a slow filling of mesopores and micropores. This hypothesis is proven by the excellent agreement of the intraparticle diffusion model plots and the textural properties of F400 activated carbon. Copyright 2009 Elsevier Ltd. All rights reserved.

Cadmium biosorption rate in protonated Sargassum biomass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, J.; Volesky, B.

1999-03-01

Biosorption of the heavy metal ion Cd{sup 2+} by protonated nonliving brown alga Sargassum fluitans biomass was accompanied by the release of hydrogen protons from the biomass. The uptake of cadmium and the release of proton matched each other throughout the biosorption process. The end-point titration methodology was used to maintain the constant pH 4.0 for developing the dynamic sorption rate. The sorption isotherm could be well represented by the Langmuir sorption model. A mass transfer model assuming the intraparticle diffusion in a one-dimensional thin plate as a controlling step was developed to describe the overall biosorption rate of cadmiummore » ions in flat seaweed biomass particles. The overall biosorption mathematical model equations were solved numerically yielding the effective diffusion coefficient D{sub e} about 3.5 {times} 10{sup {minus}6} cm{sup 2}/s. This value matches that obtained for the desorption process and is approximately half of that of the molecular diffusion coefficient for cadmium ions in aqueous solution.« less

Competitive adsorption of furfural and phenolic compounds onto activated carbon in fixed bed column.

PubMed

Sulaymon, Abbas H; Ahmed, Kawther W

2008-01-15

For a multicomponent competitive adsorption of furfural and phenolic compounds, a mathematical model was builtto describe the mass transfer kinetics in a fixed bed column with activated carbon. The effects of competitive adsorption equilibrium constant, axial dispersion, external mass transfer, and intraparticle diffusion resistance on the breakthrough curve were studied for weakly adsorbed compound (furfural) and strongly adsorbed compounds (parachlorophenol and phenol). Experiments were carried out to remove the furfural and phenolic compound from aqueous solution. The equilibrium data and intraparticle diffusion coefficients obtained from separate experiments in a batch adsorber, by fitting the experimental data with theoretical model. The results show that the mathematical model includes external mass transfer and pore diffusion using nonlinear isotherms and provides a good description of the adsorption process for furfural and phenolic compounds in a fixed bed adsorber.

Evaluation of biosurfactant obtained from Lactobacillus pentosus as foaming agent in froth flotation.

PubMed

Vecino, X; Devesa-Rey, R; Cruz, J M; Moldes, A B

2013-10-15

This study analyzes the kinetics of sediment sorption on two chemical surfactants (Tween 20 and SDS) and a biotechnologically produced surfactant (obtained from Lactobacillus pentosus). Biosurfactants were produced by fermentation of hemicellulosic sugars from vineyard pruning waste supplied as a substrate to L. pentosus. Results obtained showed that almost no SDS was adsorbed onto the sediments, whereas Tween 20 and biosurfactants from L. pentosus were absorbed after a few minutes. Kinetic models revealed that adsorption of surfactant onto riverbed sediments is governed not only by an intra-particle diffusion model (evaluated by the Weber and Morris model), but also by surface reaction models (evaluated by first, second, third order equations and Elovich equation), showing the best fit when employing the Elovich model. The adsorption properties showed by biosurfactant from L. pentosus onto sediments present it as a potential foaming agent in froth flotation. Copyright © 2013 Elsevier Ltd. All rights reserved.

Methylene blue adsorption on graphene oxide/calcium alginate composites.

PubMed

Li, Yanhui; Du, Qiuju; Liu, Tonghao; Sun, Jiankun; Wang, Yonghao; Wu, Shaoling; Wang, Zonghua; Xia, Yanzhi; Xia, Linhua

2013-06-05

Graphene oxide has been used as an adsorbent in wastewater treatment. However, the dispersibility in aqueous solution and the biotoxicity to human cells of graphene oxide limits its practical application in environmental protection. In this research, a novel environmental friendly adsorbent, calcium alginate immobilized graphene oxide composites was prepared. The effects of pH, contact time, temperature and dosage on the adsorption properties of methylene blue onto calcium alginate immobilized graphene oxide composites were investigated. The equilibrium adsorption data were described by the Langmuir and Freundlich isotherms. The maximum adsorption capacity obtained from Langmuir isotherm equation was 181.81 mg/g. The pseudo-first order, pseudo-second order, and intraparticle diffusion equation were used to evaluate the kinetic data. Thermodynamic analysis of equilibriums indicated that the adsorption reaction of methylene blue onto calcium alginate immobilized graphene oxide composites was exothermic and spontaneous in nature. Copyright © 2013 Elsevier Ltd. All rights reserved.

Removal of three nitrophenols from aqueous solutions by adsorption onto char ash: equilibrium and kinetic modeling

NASA Astrophysics Data System (ADS)

Magdy, Yehia M.; Altaher, Hossam; ElQada, E.

2018-03-01

In this research, the removal of 2,4 dinitrophenol, 2 nitrophenol and 4 nitrophenol from aqueous solution using char ash from animal bones was investigated using batch technique. Three 2-parameter isotherms (Freundlich, Langmuir, and Temkin) were applied to analyze the experimental data. Both linear and nonlinear regression analyses were performed for these models to estimate the isotherm parameters. Three 3-parameter isotherms (Redlich-Peterson, Sips, Toth) were also tested. Moreover, the kinetic data were tested using pseudo-first order, pseudo-second order, Elovich, Intraparticle diffusion and Boyd methods. Langmuir adsorption isotherm provided the best fit for the experimental data indicating monolayer adsorption. The maximum adsorption capacity was 8.624, 7.55, 7.384 mg/g for 2 nitrophenol, 2,4 dinitrophenol, and 4 nitrophenol, respectively. The experimental data fitted well to pseudo-second order model suggested a chemical nature of the adsorption process. The R 2 values for this model were 0.973 up to 0.999. This result with supported by the Temkin model indicating heat of adsorption to be greater than 10 kJ/mol. The rate controlling step was intraparticle diffusion for 2 nitrophenol, and a combination of intraparticle diffusion and film diffusion for the other two phenols. The pH and temperature of solution were found to have a considerable effect, and the temperature indicated the exothermic nature of the adsorption process. The highest adsorption capacity was obtained at pH 9 and 25 °C.

Biosorption of Cu(II) from aqueous solutions by mimosa tannin gel.

PubMed

Sengil, I Ayhan; Ozacar, Mahmut

2008-09-15

The biosorption of Cu(II) from aqueous solutions by mimosa tannin resin (MTR) was investigated as a function of particle size, initial pH, contact time and initial metal ion concentration. The aim of this study was to understand the mechanisms that govern copper removal and find a suitable equilibrium isotherm and kinetic model for the copper removal in a batch reactor. The experimental isotherm data were analysed using the Langmuir, Freundlich and Temkin equations. The equilibrium data fit well in the Langmiur isotherm. The experimental data were analysed using four sorption kinetic models -- the pseudo-first- and second-order equations, and the Elovich and the intraparticle diffusion equation -- to determine the best fit equation for the biosorption of copper ions onto mimosa tannin resin. Results show that the pseudo-second-order equation provides the best correlation for the biosorption process, whereas the Elovich equation also fits the experimental data well. Thermodynamic parameters such as the entropy change, enthalpy change and Gibb's free energy change were found out to be 153.0 J mol(-1)K(-1), 42.09 kJ mol(-1) and -2.47 kJ mol(-1), respectively.

Intra-particle migration of mercury in granular polysulfide-rubber-coated activated carbon (PSR-AC)

PubMed Central

Kim, Eun-Ah; Masue-Slowey, Yoko; Fendorf, Scott; Luthy, Richard G.

2011-01-01

The depth profile of mercuric ion after the reaction with polysulfide-rubber-coated activated carbon (PSR-AC) was investigated using micro-x-ray fluorescence (μ-XRF) imaging techniques and mathematical modeling. The μ-XRF results revealed that mercury was concentrated at 0~100 μm from the exterior of the particle after three months of treatment with PSR-AC in 10 ppm HgCl2 aqueous solution. The μ-X-ray absorption near edge spectroscopic (μ-XANES) analyses indicated HgS as a major mercury species, and suggested that the intra-particle mercury transport involved a chemical reaction with PSR polymer. An intra-particle mass transfer model was developed based on either a Langmuir sorption isotherm with liquid phase diffusion (Langmuir model) or a kinetic sorption with surface diffusion (kinetic sorption model). The Langmuir model predicted the general trend of mercury diffusion, although at a slower rate than observed from the μ-XRF map. A kinetic sorption model suggested faster mercury transport, which overestimated the movement of mercuric ions through an exchange reaction between the fast and slow reaction sites. Both μ-XRF and mathematical modeling results suggest mercury removal occurs not only at the outer surface of the PSR-AC particle but also at some interior regions due to a large PSR surface area within an AC particle. PMID:22133913

Fluorescence imaging of single-molecule retention trajectories in reversed-phase chromatographic particles.

PubMed

Cooper, Justin T; Peterson, Eric M; Harris, Joel M

2013-10-01

Due to its high specific surface area and chemical stability, porous silica is used as a support structure in numerous applications, including heterogeneous catalysis, biomolecule immobilization, sensors, and liquid chromatography. Reversed-phase liquid chromatography (RPLC), which uses porous silica support particles, has become an indispensable separations tool in quality control, pharmaceutics, and environmental analysis requiring identification of compounds in mixtures. For complex samples, the need for higher resolution separations requires an understanding of the time scale of processes responsible for analyte retention in the stationary phase. In the present work, single-molecule fluorescence imaging is used to observe transport of individual molecules within RPLC porous silica particles. This technique allows direct measurement of intraparticle molecular residence times, intraparticle diffusion rates, and the spatial distribution of molecules within the particle. On the basis of the localization uncertainty and characteristic measured diffusion rates, statistical criteria were developed to resolve the frame-to-frame behavior of molecules into moving and stuck events. The measured diffusion coefficient of moving molecules was used in a Monte Carlo simulation of a random-walk model within the cylindrical geometry of the particle diameter and microscope depth-of-field. The simulated molecular transport is in good agreement with the experimental data, indicating transport of moving molecules in the porous particle is described by a random-walk. Histograms of stuck-molecule event times, locations, and their contributions to intraparticle residence times were also characterized.

Biosorption of Food Green 3 by a novel green generation composite biosorbent from aqueous environment.

PubMed

Deniz, Fatih; Kepekci, Remziye Aysun

2017-06-03

A green type composite biosorbent composed of pine, oak, hornbeam, and fir sawdust biomasses modified with cetyltrimethylammonium bromide (CTAB) was first used for biosorption of an unsafe synthetic food dye, Food Green 3 from liquid medium in this study. Batch studies were carried by observing the effects of pH, dye concentration, biosorbent amount, and contact time. The equilibrium data were analyzed using Freundlich, Langmuir, and Dubinin-Radushkevich equations. Freundlich model gave a better conformity than other equations. The maximum dye removal potential of biosorbent was found to be 36.6 mg/g based on Langmuir isotherm. The pseudo-first-order, pseudo-second-order, Elovich, and intra-particle diffusion models were applied to clarify the process kinetics of biosorption. The mechanism studies suggested the biosorption process obeying Elovich kinetics and involving pore diffusion. The estimated values of biosorption free energy from Dubinin-Radushkevich isotherm (E value <8 kJ/mol) and thermodynamic studies (0 < ΔG° < -20 kJ/mol) implied a spontaneous, feasible, and physical process. Hence, this investigation suggested that the CTAB modified mix sawdust biomass could be a promising biosorbent for biosorption of such problematic dyes from impacted media.

Equilibrium and kinetics of adsorption of phosphate onto iron-doped activated carbon.

PubMed

Wang, Zhengfang; Nie, Er; Li, Jihua; Yang, Mo; Zhao, Yongjun; Luo, Xingzhang; Zheng, Zheng

2011-08-01

Two series of activated carbons modified by Fe (II) and Fe (III) (denoted as AC/N-Fe(II) and AC/N-Fe(III)), respectively, were used as adsorbents for the removal of phosphate in aqueous solutions. The synthesized adsorbent materials were investigated by different experimental analysis means. The adsorption of phosphate on activated carbons has been studied in kinetic and equilibrium conditions taking into account the adsorbate concentration, temperature, and solution pH as major influential factors. Maximum removals of phosphate are obtained in the pH range of 3.78-6.84 for both adsorbents. Langmuir isotherm adsorption equation well describes the experimental adsorption isotherms. Kinetic studies revealed that the adsorption process followed a pseudo-second order kinetic model. Results suggest that the main phase formed in AC/N-Fe(II) and AC/N-Fe(III) is goethite and akaganeite, respectively; the presence of iron oxides significantly affected the surface area and the pore structure of the activated carbon. Studies revealed that iron-doped activated carbons were effective in removing phosphate. AC/N-Fe(II) has a higher phosphate removal capacity than AC/N-Fe(III), which could be attributed to its better intra-particle diffusion and higher binding energy. The activation energy for adsorption was calculated to be 22.23 and 10.89 kJ mol(-1) for AC/N-Fe(II) and AC/N-Fe(III), respectively. The adsorption process was complex; both surface adsorption and intra-particle diffusion were simultaneously occurring during the process and contribute to the adsorption mechanism.

Modeling of batch sorber system: kinetic, mechanistic, and thermodynamic modeling

NASA Astrophysics Data System (ADS)

Mishra, Vishal

2017-10-01

The present investigation has dealt with the biosorption of copper and zinc ions on the surface of egg-shell particles in the liquid phase. Various rate models were evaluated to elucidate the kinetics of copper and zinc biosorptions, and the results indicated that the pseudo-second-order model was more appropriate than the pseudo-first-order model. The curve of the initial sorption rate versus the initial concentration of copper and zinc ions also complemented the results of the pseudo-second-order model. Models used for the mechanistic modeling were the intra-particle model of pore diffusion and Bangham's model of film diffusion. The results of the mechanistic modeling together with the values of pore and film diffusivities indicated that the preferential mode of the biosorption of copper and zinc ions on the surface of egg-shell particles in the liquid phase was film diffusion. The results of the intra-particle model showed that the biosorption of the copper and zinc ions was not dominated by the pore diffusion, which was due to macro-pores with open-void spaces present on the surface of egg-shell particles. The thermodynamic modeling reproduced the fact that the sorption of copper and zinc was spontaneous, exothermic with the increased order of the randomness at the solid-liquid interface.

Equilibrium and kinetic adsorption study of a cationic dye by a natural adsorbent--silkworm pupa.

PubMed

Noroozi, B; Sorial, G A; Bahrami, H; Arami, M

2007-01-02

In this work the use of silkworm pupa, which is the waste of silk spinning industries has been investigated as an adsorbent for the removal of C.I. Basic Blue 41. The amino acid nature of the pupa provided a reasonable capability for dye removal. Equilibrium adsorption isotherms and kinetics were investigated. The adsorption equilibrium data were analyzed by using various adsorption isotherm models and the results have shown that adsorption behavior of the dye could be described reasonably well by either Langmuir or Freundlich models. The characteristic parameters for each isotherm have been determined. The monolayer adsorption capacity was determined to be 555 mg/g. Kinetic studies indicated that the adsorption follows pseudo-second-order kinetics with a rate constant of 0.0434 and 0.0572 g/min mg for initial dye concentration of 200 mg/l at 20 and 40 degrees C, respectively. Kinetic studies showed that film diffusion and intra-particle diffusion were simultaneously operating during the adsorption process. The rate constant for intra-particle diffusion was estimated to be 1.985 mg/g min(0.5).

Study on the adsorption of nitrogen and phosphorus from biogas slurry by NaCl-modified zeolite

PubMed Central

Cheng, Qunpeng; Li, Hongxia; Xu, Yilu; Chen, Song; Liao, Yuhua; Deng, Fang; Li, Jianfen

2017-01-01

A NaCl-modified zeolite was used to simultaneously remove nitrogen and phosphate from biogas slurry. The effect of pH, contact time and dosage of absorbants on the removal efficiency of nitrogen and phosphate were studied. The results showed that the highest removal efficiency of NH4+-N (92.13%) and PO43−-P (90.3%) were achieved at pH 8. While the zeolite doses ranged from 0.5 to 5 g/100 ml, NH4+-N and PO43−-P removal efficiencies ranged from 5.19% to 94.94% and 72.16% to 91.63% respectively. The adsorption isotherms of N and P removal with NaCl-modified zeolite were well described by Langmuir models, suggesting the homogeneous sorption mechanisms. While through intra-particle diffusion model to analyze the influence of contact time, it showed that the adsorption process of NH4+-N and PO43−-P followed the second step of intra-particle diffusion model. The surface diffusion adsorption step was very fast which was finished in a short time. PMID:28542420

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buitrago, Paula A.; Morrill, Mike; Lighty, JoAnn S.

This report presents experimental and modeling mercury oxidation and adsorption data. Fixed-bed and single-particle models of mercury adsorption were developed. The experimental data were obtained with two reactors: a 300-W, methane-fired, tubular, quartz-lined reactor for studying homogeneous oxidation reactions and a fixed-bed reactor, also of quartz, for studying heterogeneous reactions. The latter was attached to the exit of the former to provide realistic combustion gases. The fixed-bed reactor contained one gram of coconut-shell carbon and remained at a temperature of 150°C. All methane, air, SO 2, and halogen species were introduced through the burner to produce a radical pool representativemore » of real combustion systems. A Tekran 2537A Analyzer coupled with a wet conditioning system provided speciated mercury concentrations. At 150°C and in the absence of HCl or HBr, the mercury uptake was about 20%. The addition of 50 ppm HCl caused complete capture of all elemental and oxidized mercury species. In the absence of halogens, SO 2 increased the mercury adsorption efficiency to up to 30 percent. The extent of adsorption decreased with increasing SO 2 concentration when halogens were present. Increasing the HCl concentration to 100 ppm lessened the effect of SO 2. The fixed-bed model incorporates Langmuir adsorption kinetics and was developed to predict adsorption of elemental mercury and the effect of multiple flue gas components. This model neglects intraparticle diffusional resistances and is only applicable to pulverized carbon sorbents. It roughly describes experimental data from the literature. The current version includes the ability to account for competitive adsorption between mercury, SO 2, and NO 2. The single particle model simulates in-flight sorbent capture of elemental mercury. This model was developed to include Langmuir and Freundlich isotherms, rate equations, sorbent feed rate, and intraparticle diffusion. The Freundlich isotherm more accurately described in-flight mercury capture. Using these parameters, very little intraparticle diffusion was evident. Consistent with other data, smaller particles resulted in higher mercury uptake due to available surface area. Therefore, it is important to capture the particle size distribution in the model. At typical full-scale sorbent feed rates, the calculations under-predicted adsorption, suggesting that wall effects can account for as much as 50 percent of the removal, making it an important factor in entrained-mercury adsorption models.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buitrago, Paula A.; Morrill, Mike; Lighty, JoAnn S.

This report presents experimental and modeling mercury oxidation and adsorption data. Fixed-bed and single-particle models of mercury adsorption were developed. The experimental data were obtained with two reactors: a 300-W, methane-fired, tubular, quartz-lined reactor for studying homogeneous oxidation reactions and a fixed-bed reactor, also of quartz, for studying heterogeneous reactions. The latter was attached to the exit of the former to provide realistic combustion gases. The fixed-bed reactor contained one gram of coconut-shell carbon and remained at a temperature of 150°C. All methane, air, SO 2, and halogen species were introduced through the burner to produce a radical pool representativemore » of real combustion systems. A Tekran 2537A Analyzer coupled with a wet conditioning system provided speciated mercury concentrations. At 150°C and in the absence of HCl or HBr, the mercury uptake was about 20%. The addition of 50 ppm HCl caused complete capture of all elemental and oxidized mercury species. In the absence of halogens, SO 2 increased the mercury adsorption efficiency to up to 30 percent. The extent of adsorption decreased with increasing SO 2 concentration when halogens were present. Increasing the HCl concentration to 100 ppm lessened the effect of SO 2. The fixed-bed model incorporates Langmuir adsorption kinetics and was developed to predict adsorption of elemental mercury and the effect of multiple flue gas components. This model neglects intraparticle diffusional resistances and is only applicable to pulverized carbon sorbents. It roughly describes experimental data from the literature. The current version includes the ability to account for competitive adsorption between mercury, SO 2, and NO 2. The single particle model simulates in-flight sorbent capture of elemental mercury. This model was developed to include Langmuir and Freundlich isotherms, rate equations, sorbent feed rate, and intraparticle diffusion. The Freundlich isotherm more accurately described in-flight mercury capture. Using these parameters, very little intraparticle diffusion was evident. Consistent with other data, smaller particles resulted in higher mercury uptake due to available surface area. Therefore, it is important to capture the particle size distribution in the model. At typical full-scale sorbent feed rates, the calculations underpredicted adsorption, suggesting that wall effects can account for as much as 50 percent of the removal, making it an important factor in entrained-mercury adsorption models.« less

Adsorption of direct dyes from aqueous solutions by carbon nanotubes: determination of equilibrium, kinetics and thermodynamics parameters.

PubMed

Kuo, Chao-Yin; Wu, Chung-Hsin; Wu, Jane-Yii

2008-11-15

This study examined the feasibility of removing direct dyes C.I. Direct Yellow 86 (DY86) and C.I. Direct Red 224 (DR224) from aqueous solutions using carbon nanotubes (CNTs). The effects of dye concentration, CNT dosage, ionic strength and temperature on adsorption of direct dyes by CNTs were also evaluated. Pseudo second-order, intraparticle diffusion and Bangham models were adopted to evaluate experimental data and thereby elucidate the kinetic adsorption process. Additionally, this study used the Langmuir, Freundlich, Dubinin and Radushkevich (D-R) and Temkin isotherms to describe equilibrium adsorption. The adsorption percentage of direct dyes increased as CNTs dosage, NaCl addition and temperature increased. Conversely, the adsorption percentage of direct dyes decreased as dye concentration increased. The pseudo second-order model best represented adsorption kinetics. Based on the regressions of intraparticle diffusion and Bangham models, experimental data suggest that the adsorption of direct dyes onto CNTs involved intraparticle diffusion, but that was not the only rate-controlling step. The equilibrium adsorption of DR86 is best fitted in the Freundlich isotherm and that of DR224 was best fitted in the D-R isotherm. The capacity of CNTs to adsorb DY86 and DR224 was 56.2 and 61.3 mg/g, respectively. For DY86, enthalpy (DeltaH(0)) and entropy (DeltaS(0)) were 13.69 kJ/mol and 139.51 J/mol K, respectively, and those for DR224 were 24.29 kJ/mol and 172.06 J/mol K, respectively. The values of DeltaH(0), DeltaG(0) and E all indicate that the adsorption of direct dyes onto CNTs was a physisorption process.

EFFECT OF MOLECULAR OXYGEN ON THE SCALEUP OF GAC ADSORBERS

EPA Science Inventory

A rapid small-scale column test (RSSCT), designed according to the assumption of no dependency of the intraparticle surface diffusion coefficient on the activated carbon particle size, was able to accurately predict breakthrough of three volatile organic chemicals as well as back...

Effective adsorption of phenolic compound from aqueous solutions on activated semi coke

NASA Astrophysics Data System (ADS)

Gao, Xiaoming; Dai, Yuan; Zhang, Yu; Fu, Feng

2017-03-01

Activated Semi coke was prepared by KOH activation and employed as adsorbent to study adsorption function of phenolic compound from aqueous solutions. The adsorption result showed that the adsorption capacity of the activated semi coke for phenolic compound increased with contact time and adsorbent dosage, and slightly affected by temperature. The surface structure property of the activated semi coke was characterized by N2 adsorption, indicating that the activated semi coke was essentially macroporous, and the BET surface area was 347.39 m2 g-1. Scanning electron microscopy indicated that the surface of the activated semi coke had a high developed pore. The adsorption kinetics were investigated according to pseudofirst order, pseudosecond order and intraparticle diffusion, and the kinetics data were fitted by pseudosecond order model, and intraparticle diffusion was not the only rate-controlling step. Adsorption isotherm was studied by Langmuir, Freundlich, Temkin, Redlich-Peterson, Sips and Toth models. The result indicated that adsorption isotherm data could fit well with Langmuir, Redlich-Peterson, Sips and Toth models.

Comparative study on kinetic adsorption of Cu(II), Cd(II) and Ni(II) ions from aqueous solutions using activated sludge and dried sludge

NASA Astrophysics Data System (ADS)

Ong, Soon-An; Toorisaka, Eiichi; Hirata, Makoto; Hano, Tadashi

2013-03-01

The adsorption of Cu(II), Cd(II) and Ni(II) ions from aqueous solutions by activated sludge and dried sludge was investigated under laboratory conditions to assess its potential in removing metal ions. The adsorption behavior of metal ions onto activated sludge and dried sludge was analyzed with Weber-Morris intra-particle diffusion model, Lagergren first-order model and pseudo second-order model. The rate constant of intra-particle diffusion on activated sludge and dried sludge increased in the sequence of Cu(II) > Ni(II) > Cd(II). According to the regression coefficients, it was observed that the kinetic adsorption data can fit better by the pseudo second-order model compared to the first-order Lagergren model with R 2 > 0.997. The adsorption capacities of metal ions onto activated sludge and dried sludge followed the sequence Ni(II) ≈ Cu(II) > Cd(II) and Cu(II) > Ni(II) > Cd(II).

Preparation and characterization of corn cob activated carbon coated with nano-sized magnetite particles for the removal of Cr(VI).

PubMed

Nethaji, S; Sivasamy, A; Mandal, A B

2013-04-01

Activated carbon prepared from corn cob biomass, magnetized by magnetite nanoparticles (MCCAC) was used for the adsorption of hexavalent chromium from aqueous solution. The adsorbent was characterized by SEM, TEM, XRD, VSM, surface functionality and zero-point charge. The iron oxide nanoparticles were of 50 nm sizes and the saturation magnetization value for the adsorbent is 48.43 emu/g. Adsorption was maximum at pH 2. Isotherm data were modeled using Langmuir, Freundlich and Temkin isotherm. The prepared MCCAC had a heterogeneous surface. The maximum monolayer adsorption capacity was 57.37 mg/g. Kinetic studies were carried out and the data fitted the pseudo second-order equation. The mechanism of the adsorption process was studied by incorporating the kinetic data with intraparticle diffusion model, Bangham equation and Boyd plot. The adsorption was by chemisorption and the external mass transfer was the rate-determining step. A micro column was designed and the basic column parameters were estimated. Copyright © 2013 Elsevier Ltd. All rights reserved.

Separation of toxic rhodamine B from aqueous solution using an efficient low-cost material, Azolla pinnata, by adsorption method.

PubMed

Kooh, Muhammad Raziq Rahimi; Lim, Linda B L; Lim, Lee Hoon; Dahri, Muhammad Khairud

2016-02-01

This study investigated the potential of untreated Azolla pinnata (AP) to remove toxic rhodamine B (RB) dye. The effects of adsorbent dosage, pH, ionic strength, contact time, and concentration were studied. Experiments involving the effects of pH and ionic strength indicated that hydrophobic-hydrophobic interactions might be the dominant force of attraction for the RB-AP adsorption system. The kinetics modelling of the kinetics experiment showed that pseudo-second-order best represented the adsorption process. The Weber-Morris intraparticle diffusion model showed that intraparticle diffusion is not the rate-limiting step, while the Boyd model suggested that film diffusion might be rate-limiting. The adsorption isotherm model, Langmuir, best represented the adsorption process, and the maximum adsorption capacity was predicted to be 72.2 and 199.7 mg g(-1) at 25 and 65 °C, respectively. Thermodynamics study indicates spontaneity, endothermic and physisorption-dominant adsorption process. The adsorbents were regenerated to satisfactory level with distilled water, HNO3 and NaOH. Pre-treatment of adsorbent with oxalic acid, citric acid, NaOH, HCl and phosphoric acid was investigated but the adsorption capacity was less than the untreated AP.

Adsorption of anionic and cationic dyes on activated carbon from aqueous solutions: equilibrium and kinetics.

PubMed

Rodríguez, Araceli; García, Juan; Ovejero, Gabriel; Mestanza, María

2009-12-30

Activated carbon was utilized as adsorbent to remove anionic dye, Orange II (OII), and cationic dye, Methylene blue (MB), from aqueous solutions by adsorption. Batch experiments were conducted to study the effects of temperature (30-65 degrees C), initial concentration of adsorbate (300-500 mg L(-1)) and pH (3.0-9.0) on dyes adsorption. Equilibrium adsorption isotherms and kinetics were investigated. The equilibrium experimental data were analyzed by the Langmuir, Freundlich, Toth and Redlich-Peterson models. The kinetic data obtained with different carbon mass were analyzed using a pseudo-first order, pseudo-second order, intraparticle diffusion, Bangham and Chien-Clayton equations. The best results were achieved with the Langmuir isotherm equilibrium model and with the pseudo-second order kinetic model. The activated carbon was found to be very effective as adsorbent for MB and OII from aqueous solutions.

Modeling packed bed sorbent systems with the Pore Surface Diffusion Model: Evidence of facilitated surface diffusion of arsenate in nano-metal (hydr)oxide hybrid ion exchange media.

PubMed

Dale, Sachie; Markovski, Jasmina; Hristovski, Kiril D

2016-09-01

This study explores the possibility of employing the Pore Surface Diffusion Model (PSDM) to predict the arsenic breakthrough curve of a packed bed system operated under continuous flow conditions with realistic groundwater, and consequently minimize the need to conduct pilot scale tests. To provide the nano-metal (hydr)oxide hybrid ion exchange media's performance in realistic water matrices without engaging in taxing pilot scale testing, the multi-point equilibrium batch sorption tests under pseudo-equilibrium conditions were performed; arsenate breakthrough curve of short bed column (SBC) was predicted by the PSDM in the continuous flow experiments; SBC tests were conducted under the same conditions to validate the model. The overlapping Freundlich isotherms suggested that the water matrix and competing ions did not have any denoting effect on sorption capacity of the media when the matrix was changed from arsenic-only model water to real groundwater. As expected, the PSDM provided a relatively good prediction of the breakthrough profile for arsenic-only model water limited by intraparticle mass transports. In contrast, the groundwater breakthrough curve demonstrated significantly faster intraparticle mass transport suggesting to a surface diffusion process, which occurs in parallel to the pore diffusion. A simple selection of DS=1/2 DP appears to be sufficient when describing the facilitated surface diffusion of arsenate inside metal (hydr)oxide nano-enabled hybrid ion-exchange media in presence of sulfate, however, quantification of the factors determining the surface diffusion coefficient's magnitude under different treatment scenarios remained unexplored. Copyright © 2015 Elsevier B.V. All rights reserved.

Treatment of wastewater containing toxic chromium using new activated carbon developed from date palm seed.

PubMed

El Nemr, Ahmed; Khaled, Azza; Abdelwahab, Ola; El-Sikaily, Amany

2008-03-21

The use of a new activated carbon developed from date palm seed wastes, generated in the jam industry, for removing toxic chromium from aqueous solution has been investigated. The activated carbon has been achieved from date palm seed by dehydrating methods using concentrated sulfuric acid. The batch experiments were conducted to determine the adsorption capacity of the biomass. The effect of initial metal concentration (25-125mgl(-1)), pH, contact time, and concentration of date palm seed carbon have been studied at room temperature. A strong dependence of the adsorption capacity on pH was observed, the capacity increase as pH value decrease and the optimum pH value is pH 1.0. Kinetics and adsorption equilibrium were studied at different sorbent doses. The adsorption process was fast and the equilibrium was reached within 180min. The maximum removal was 100% for 75mgl(-1) of Cr(+ concentration on 4gl(-1) carbon concentration and the maximum adsorption capacity was 120.48mgg(-1). The kinetic data were analyzed using various kinetic models - pseudo-first order equation, pseudo-second order equation, Elovich equation and intraparticle diffusion equation - and the equilibrium data were tested using several isotherm models, Langmuir, Freundlich, Koble-Corrigan, Redlich-Peterson, Tempkin, Dubinin-Radushkevich and Generalized isotherm equations. The Elovich equation and pseudo-second order equation provide the greatest accuracy for the kinetic data and Koble-Corrigan and Langmuir models the closest fit for the equilibrium data. Activation energy of sorption has also been evaluated as 0.115 and 0.229kJmol(-1).

Kinetic, equilibrium and thermodynamic studies on sorption of uranium and thorium from aqueous solutions by a selective impregnated resin containing carminic acid.

PubMed

Rahmani-Sani, Abolfazl; Hosseini-Bandegharaei, Ahmad; Hosseini, Seyyed-Hossein; Kharghani, Keivan; Zarei, Hossein; Rastegar, Ayoob

2015-04-09

In this work, the removal of uranium and thorium ions from aqueous solutions was studied by solid-liquid extraction using an advantageous extractant-impregnated resin (EIR) prepared by loading carminic acid (CA) onto Amberlite XAD-16 resin beads. Batch sorption experiments using CA/XAD-16 beads for the removal of U(VI) and Th(IV) ions were carried out as a function of several parameters, like equilibration time, metal ion concentration, etc. The equilibrium data obtained from the sorption experiments were adjusted to the Langmuir isotherm model and the calculated maximum sorption capacities in terms of monolayer sorption were in agreement with those obtained from the experiments. The experimental data on the sorption behavior of both metal ions onto the EIR beads fitted well in both Bangham and intra-particle diffusion kinetic models, indicating that the intra-particle diffusion is the rate-controlling step. The thermodynamic studies at different temperatures revealed the feasibility and the spontaneous nature of the sorption process for both uranium and thorium ions. Copyright © 2014 Elsevier B.V. All rights reserved.

Novel biosynthesized silver nanoparticles from cobweb as adsorbent for Rhodamine B: equilibrium isotherm, kinetic and thermodynamic studies

NASA Astrophysics Data System (ADS)

Azeez, Luqmon; Lateef, Agbaje; Adebisi, Segun A.; Oyedeji, Abdulrasaq O.

2018-03-01

This study has investigated the adsorption of Rhodamine B (Rh-B) dye on novel biosynthesized silver nanoparticles (AgNPs) from cobweb. The effects of contact time, initial pH, initial dye concentration, adsorbent dosage and temperature were studied on the removal of Rh-B and they significantly affected its uptake. Adsorption isotherms were evaluated using Langmuir, Freundlich, Temkin and Dubinin-Radushkevich isotherm models. The adsorption process was best described by Langmuir isotherm with R 2 of 0.9901, indicating monolayer adsorption. The maximum adsorption capacity ( q max) of 59.85 mg/g showed that it has relatively high performance, while adsorption intensity showed a favourable adsorption process. Pseudo-second-order kinetics fitted best the rate of adsorption and intra-particle diffusion revealed both surface adsorption and intra-particle diffusion-controlled adsorption process. Negative values of thermodynamic parameters (Δ H°, Δ S° and Δ G°) indicated an exothermic and spontaneous adsorption process. The mean sorption energy ( E) and activation energy ( E a) suggested the uptake of Rh-B onto AgNPs was chemical in nature (chemosorption).

Guava (Psidium guajava) leaf powder: novel adsorbent for removal of methylene blue from aqueous solutions.

PubMed

Ponnusami, V; Vikram, S; Srivastava, S N

2008-03-21

Batch sorption experiments were carried out using a novel adsorbent, guava leaf powder (GLP), for the removal of methylene blue (MB) from aqueous solutions. Potential of GLP for adsorption of MB from aqueous solution was found to be excellent. Effects of process parameters pH, adsorbent dosage, concentration, particle size and temperature were studied. Temperature-concentration interaction effect on dye uptake was studied and a quadratic model was proposed to predict dye uptake in terms of concentration, time and temperature. The model conforms closely to the experimental data. The model was used to find optimum temperature and concentration that result in maximum dye uptake. Langmuir model represent the experimental data well. Maximum dye uptake was found to be 295mg/g, indicating that GLP can be used as an excellent low-cost adsorbent. Pseudo-first-order, pseudo-second order and intraparticle diffusion models were tested. From experimental data it was found that adsorption of MB onto GLP follow pseudo second order kinetics. External diffusion and intraparticle diffusion play roles in adsorption process. Free energy of adsorption (DeltaG degrees ), enthalpy change (DeltaH degrees ) and entropy change (DeltaS degrees ) were calculated to predict the nature of adsorption. Adsorption in packed bed was also evaluated.

Enhanced adsorptive removal of p-nitrophenol from water by aluminum metal-organic framework/reduced graphene oxide composite

NASA Astrophysics Data System (ADS)

Wu, Zhibin; Yuan, Xingzhong; Zhong, Hua; Wang, Hou; Zeng, Guangming; Chen, Xiaohong; Wang, Hui; Zhang, Lei; Shao, Jianguang

2016-05-01

In this study, the composite of aluminum metal-organic framework MIL-68(Al) and reduced graphene oxide (MA/RG) was synthesized via a one-step solvothermal method, and their performances for p-nitrophenol (PNP) adsorption from aqueous solution were systematically investigated. The introduction of reduced graphene oxide (RG) into MIL-68(Al) (MA) significantly changes the morphologies of the MA and increases the surface area. The MA/RG-15% prepared at RG-to-MA mass ratio of 15% shows a PNP uptake rate 64% and 123% higher than MIL-68(Al) and reduced graphene oxide (RG), respectively. The hydrogen bond and π - π dispersion were considered to be the major driving force for the spontaneous and endothermic adsorption process for PNP removal. The adsorption kinetics, which was controlled by film-diffusion and intra-particle diffusion, was greatly influenced by solution pH, ionic strength, temperature and initial PNP concentration. The adsorption kinetics and isotherms can be well delineated using pseudo-second-order and Langmuir equations, respectively. The presence of phenol or isomeric nitrophenols in the solution had minimal influence on PNP adsorption by reusable MA/RG composite.

Study of Adsorption Mechanism of Congo Red on Graphene Oxide/PAMAM Nanocomposite

PubMed Central

Rafi, Mohammad; Samiey, Babak; Cheng, Chil-Hung

2018-01-01

Graphene oxide/poly(amidoamine) (GO/PAMAM) nanocomposite adsorbed high quantities of congo red (CR) anionic dye in 0.1 M NaCl solution, with the maximum adsorption capacity of 198 mg·g−1. The kinetics and thermodynamics of adsorption were investigated to elucidate the effects of pH, temperature, shaking rate, ionic strength, and contact time. Kinetic data were analyzed by the KASRA model and the KASRA, ISO, and pore-diffusion equations. Adsorption adsorption isotherms were studied by the ARIAN model and the Henry, Langmuir, and Temkin equations. It was shown that adsorption sites of GO/PAMAM at experimental conditions were phenolic hydroxyl groups of GO sheets and terminal amine groups of PAMAM dendrimer. Analysis of kinetic data indicated that amine sites were located on the surface, and that hydroxyl sites were placed in the pores of adsorbent. CR molecules interacted with the adsorption sites via hydrogen bonds. The molecules were adsorbed firstly on the amine sites, and then on the internal hydroxyl sites. Adsorption kinetic parameters indicated that the interaction of CR to the –NH3+ sites was the rate-controlling step of adsorption of CR on this site and adsorption activation energies calculated for different parts of this step. On the other hand, kinetic parameters showed that the intraparticle diffusion was the rate-controlling step during the interaction of CR molecules to –OH sites and activation energy of this step was not calculable. Finally, the used GO/PAMAM was completely regenerated by using ethylenediamine. PMID:29587463

Boron removal by a composite sorbent: Polyethylenimine/tannic acid derivative immobilized in alginate hydrogel beads.

PubMed

Bertagnolli, Caroline; Grishin, Andrey; Vincent, Thierry; Guibal, Eric

2017-03-21

A novel composite material was prepared by the grafting of tannic acid on polyethylenimine (PEI), which allows an efficient sorption of boron (sorption capacity close to 0.89 mmol B g -1 ). The encapsulation of this chelating sorbent (finely crushed) facilitates its use (readily solid/liquid separation, use in fixed-bed columns) at the expense of a loss in sorption capacity (proportionally decreased by the introduction of alginate having poor efficiency for boron uptake). Sorption isotherms are modeled using the Langmuir equation, while the kinetic profiles are presented a good fit by pseudo-second order rate equation. In addition, the encapsulating matrix introduces supplementary resistance to intraparticle diffusion, especially when the resin is dried without control: freeze-drying partially limits this effect. The stability (at long-term storage) of the sorbent is improved when the sorbent is stored under nitrogen atmosphere. The presence of an excess of NaCl was investigated. The degradation of the hydrogel (by ion-exchange of Ca(II) with Na(I)) leads to a decrease in the sorption performance of composite material but the action of Ca(II) ions in the solutions re-stabilizes the hydrogel.

Phosphorus removal from aqueous solution in parent and aluminum-modified eggshells: thermodynamics and kinetics, adsorption mechanism, and diffusion process.

PubMed

Guo, Ziyan; Li, Jiuhai; Guo, Zhaobing; Guo, Qingjun; Zhu, Bin

2017-06-01

Parent and aluminum-modified eggshells were prepared and characterized with X-ray diffraction, specific surface area measurements, infrared spectroscopy, zeta potential, and scanning electron microscope, respectively. Besides, phosphorus adsorptions in these two eggshells at different temperatures and solution pH were carried out to study adsorption thermodynamics and kinetics as well as the mechanisms of phosphorus adsorption and diffusion. The results indicated that high temperature was favorable for phosphorus adsorption in parent and aluminum-modified eggshells. Alkaline solution prompted phosphorus adsorption in parent eggshell, while the maximum adsorption amount was achievable at pH 4 in aluminum-modified eggshell. Adsorption isotherms of phosphorus in these eggshells could be well described by Langmuir and Freundlich models. Phosphorus adsorption amounts in aluminum-modified eggshell were markedly higher compared to those in parent eggshell. Adsorption heat indicated that phosphorus adsorption in parent eggshell was a typically physical adsorption process, while chemical adsorption mechanism of ion exchange between phosphorus and hydroxyl groups on the surface of eggshells was dominated in aluminum-modified eggshell. The time-resolved uptake curves showed phosphorus adsorption in aluminum-modified eggshell was significantly faster than that in parent eggshell. Moreover, there existed two clear steps in time-resolved uptake curves of phosphorus in parent eggshell. Based on pseudo-second order kinetic model and intraparticle diffusion model, we inferred more than one process affected phosphorus adsorption. The first process was the diffusion of phosphorus through water to external surface and the opening of pore channel in the eggshells, and the second process was mainly related to intraparticle diffusion.

External and Intraparticle Diffusion of Coumarin 102 with Surfactant in the ODS-silica Gel/water System by Single Microparticle Injection and Confocal Fluorescence Microspectroscopy.

PubMed

Nakatani, Kiyoharu; Matsuta, Emi

2015-01-01

The release mechanism of coumarin 102 from a single ODS-silica gel microparticle into the water phase in the presence of Triton X-100 was investigated by confocal fluorescence microspectroscopy combined with the single microparticle injection technique. The release rate significantly depended on the Triton X-100 concentration in the water phase and was not limited by diffusion in the pores of the microparticle. The release rate constant was inversely proportional to the microparticle radius squared, indicating that the rate-determining step is the external diffusion between the microparticle and the water phase.

The quantitative impact of the mesopore size on the mass transfer mechanism of the new 1.9μm fully porous Titan-C18 particles. I: analysis of small molecules.

PubMed

Gritti, Fabrice; Guiochon, Georges

2015-03-06

Previous data have shown that could deliver a minimum reduced plate height as small as 1.7. Additionally, the reduction of the mesopore size after C18 derivatization and the subsequent restriction for sample diffusivity across the Titan-C18 particles were found responsible for the unusually small value of the experimental optimum reduced velocity (5 versus 10 for conventional particles) and for the large values of the average reduced solid-liquid mass transfer resistance coefficients (0.032 versus 0.016) measured for a series of seven n-alkanophenones. The improvements in column efficiency made by increasing the average mesopore size of the Titan silica from 80 to 120Å are investigated from a quantitative viewpoint based on the accurate measurements of the reduced coefficients (longitudinal diffusion, trans-particle mass transfer resistance, and eddy diffusion) and of the intra-particle diffusivity, pore, and surface diffusion for the same series of n-alkanophenone compounds. The experimental results reveal an increase (from 0% to 30%) of the longitudinal diffusion coefficients for the same sample concentration distribution (from 0.25 to 4) between the particle volume and the external volume of the column, a 40% increase of the intra-particle diffusivity for the same sample distribution (from 1 to 7) between the particle skeleton volume and the bulk phase, and a 15-30% decrease of the solid-liquid mass transfer coefficient for the n-alkanophenone compounds. Pore and surface diffusion are increased by 60% and 20%, respectively. The eddy dispersion term and the maximum column efficiency (295000plates/m) remain virtually unchanged. The rate of increase of the total plate height with increasing the chromatographic speed is reduced by 20% and it is mostly controlled (75% and 70% for 80 and 120Å pore size) by the flow rate dependence of the eddy dispersion term. Copyright © 2015 Elsevier B.V. All rights reserved.

Advective removal of intraparticle uranium from contaminated vadose zone sediments, Hanford, U.S.

PubMed

Ilton, Eugene S; Qafoku, Nikolla P; Liu, Chongxuan; Moore, Dean A; Zachara, John M

2008-03-01

A column study on U(VI)-contaminated vadose zone sediments from the Hanford Site, WA, was performed to investigate U(VI) release kinetics with water advection and variable geochemical conditions. The sediments were collected from an area adjacent to and below tank BX-102 that was contaminated as a result of a radioactive tank waste overfill event. The primary reservoir for U(VI) in the sediments are micrometer-size precipitates composed of nanocrystallite aggregates of a Na-U-Silicate phase, most likely Na-boltwoodite, that nucleated and grew within microfractures of the plagioclase component of sand-sized granitic clasts. Two sediment samples, with different U(VI) concentrations and intraparticle mass transfer properties, were leached with advective flows of three different solutions. The influent solutions were all calcite-saturated and in equilibrium with atmospheric CO2. One solution was prepared from DI water, the second was a synthetic groundwater (SGW) with elevated Na that mimicked groundwater at the Hanford site, and the third was the same SGW but with both elevated Na and Si. The latter two solutions were employed, in part, to test the effect of saturation state on U(VI) release. For both sediments, and all three electrolytes, there was an initial rapid release of U(VI) to the advecting solution followed by slower near steady-state release. U(VI)aq concentrations increased during subsequent stop-flow events. The electrolytes with elevated Na and Si depressed U(VL)aq concentrations in effluent solutions. Effluent U(VI)aq concentrations for both sediments and all three electrolytes were simulated reasonably well by a three domain model (the advecting fluid, fractures, and matrix) that coupled U(VI) dissolution, intraparticle U(VI)aq diffusion, and interparticle advection, where diffusion and dissolution properties were parameterized in a previous batch study.

Citric acid modified kenaf core fibres for removal of methylene blue from aqueous solution.

PubMed

Sajab, Mohd Shaiful; Chia, Chin Hua; Zakaria, Sarani; Jani, Saad Mohd; Ayob, Mohd Khan; Chee, Kah Leong; Khiew, Poi Sim; Chiu, Wee Siong

2011-08-01

Chemically modified kenaf core fibres were prepared via esterification in the presence of citric acid (CA). The adsorption kinetics and isotherm studies were carried out under different conditions to examine the adsorption efficiency of CA-treated kenaf core fibres towards methylene blue (MB). The adsorption capacity of the kenaf core fibres increased significantly after the citric acid treatment. The values of the correlation coefficients indicated that the Langmuir isotherm fitted the experimental data better than the Freundlich isotherm. The maximum adsorption capacity of the CA-treated kenaf core fibres was found to be 131.6mg/g at 60°C. Kinetic models, pseudo-first-order, pseudo-second-order and intraparticle diffusion, were employed to describe the adsorption mechanism. The kinetic data were found to fit pseudo-second-order model equation as compared to pseudo-first-order model. The adsorption of MB onto the CA-treated kenaf core fibres was spontaneous and endothermic. Copyright © 2011 Elsevier Ltd. All rights reserved.

Treatment of aqueous diethyl phthalate by adsorption using a functional polymer resin.

PubMed

Xu, Zhengwen; Zhang, Weiming; Pan, Bingcai; Lv, Lu; Jiang, Zhengmao

2011-01-01

To study the adsorptive separation efficiency, adsorption and desorption performances of diethyl phthalate (DEP) were investigated with a functional polymer resin (NDA-702). A macroporous polymer resin (XAD-4) and a coal-based granular activated carbon (AC-750) were chosen for comparison. The kinetic adsorption data obeyed the pseudo-second-order rate model, and the adsorption processes were limited by both film and intraparticle diffusions. Adsorption equilibrium data were well fitted by the Freundlich equation, and the larger uptake and higher selection of NDA-702 than AC-750 and XAD-4 was probably due to the microporous structure, phenyl rings and polar groups on NDA-702. Thermodynamic adsorption studies indicated that the test adsorbents spontaneously adsorbed DEP, driven mainly by enthalpy change. Continuous fixed-bed runs demonstrated that there no significant loss of the resin's adsorption capacity and there was complete regeneration of NDA-702. The results suggest that NDA-702 has excellent potential as an adsorption material for water treatment.

Utilization of oil palm biodiesel solid residue as renewable sources for preparation of granular activated carbon by microwave induced KOH activation.

PubMed

Foo, K Y; Hameed, B H

2013-02-01

In this work, preparation of granular activated carbon from oil palm biodiesel solid residue, oil palm shell (PSAC) by microwave assisted KOH activation has been attempted. The physical and chemical properties of PSAC were characterized using scanning electron microscopy, volumetric adsorption analyzer and elemental analysis. The adsorption behavior was examined by performing batch adsorption experiments using methylene blue as dye model compound. Equilibrium data were simulated using the Langmuir, Freundlich and Temkin isotherm models. Kinetic modeling was fitted to the pseudo-first-order, pseudo-second-order and Elovich kinetic models, while the adsorption mechanism was determined using the intraparticle diffusion and Boyd equations. The result was satisfactory fitted to the Langmuir isotherm model with a monolayer adsorption capacity of 343.94mg/g at 30°C. The findings support the potential of oil palm shell for preparation of high surface area activated carbon by microwave assisted KOH activation. Copyright © 2012 Elsevier Ltd. All rights reserved.

Adsorption of methylene blue onto activated carbon produced from tea (Camellia sinensis L.) seed shells: kinetics, equilibrium, and thermodynamics studies.

PubMed

Gao, Jun-Jie; Qin, Ye-Bo; Zhou, Tao; Cao, Dong-Dong; Xu, Ping; Hochstetter, Danielle; Wang, Yue-Fei

2013-07-01

Tea (Camellia sinensis L.) seed shells, the main byproduct of the manufacture of tea seed oil, were used as precursors for the preparation of tea activated carbon (TAC) in the present study. A high yield (44.1%) of TAC was obtained from tea seed shells via a one-step chemical method using ZnCl2 as an agent. The Brunauer-Emmett-Teller (BET) surface area and the total pore volumes of the obtained TAC were found to be 1530.67 mg(2)/g and 0.7826 cm(3)/g, respectively. The equilibrium adsorption results were complied with Langmuir isotherm model and its maximum monolayer adsorption capacity was 324.7 mg/g for methylene blue. Adsorption kinetics studies indicated that the pseudo-second-order model yielded the best fit for the kinetic data. An intraparticle diffusion model suggested that the intraparticle diffusion was not the only rate-controlling step. Thermodynamics studies revealed the spontaneous and exothermic nature of the sorption process. These results indicate that tea seed shells could be utilized as a renewable resource to develop activated carbon which is a potential adsorbent for methylene blue.

Adsorption of methylene blue onto activated carbon produced from tea (Camellia sinensis L.) seed shells: kinetics, equilibrium, and thermodynamics studies*

PubMed Central

Gao, Jun-jie; Qin, Ye-bo; Zhou, Tao; Cao, Dong-dong; Xu, Ping; Hochstetter, Danielle; Wang, Yue-fei

2013-01-01

Tea (Camellia sinensis L.) seed shells, the main byproduct of the manufacture of tea seed oil, were used as precursors for the preparation of tea activated carbon (TAC) in the present study. A high yield (44.1%) of TAC was obtained from tea seed shells via a one-step chemical method using ZnCl2 as an agent. The Brunauer-Emmett-Teller (BET) surface area and the total pore volumes of the obtained TAC were found to be 1 530.67 mg2/g and 0.782 6 cm3/g, respectively. The equilibrium adsorption results were complied with Langmuir isotherm model and its maximum monolayer adsorption capacity was 324.7 mg/g for methylene blue. Adsorption kinetics studies indicated that the pseudo-second-order model yielded the best fit for the kinetic data. An intraparticle diffusion model suggested that the intraparticle diffusion was not the only rate-controlling step. Thermodynamics studies revealed the spontaneous and exothermic nature of the sorption process. These results indicate that tea seed shells could be utilized as a renewable resource to develop activated carbon which is a potential adsorbent for methylene blue. PMID:23825151

Kinetic and calorimetric study of the adsorption of dyes on mesoporous activated carbon prepared from coconut coir dust.

PubMed

Macedo, Jeremias de Souza; da Costa Júnior, Nivan Bezerra; Almeida, Luis Eduardo; Vieira, Eunice Fragoso da Silva; Cestari, Antonio Reinaldo; Gimenez, Iara de Fátima; Villarreal Carreño, Neftali Lênin; Barreto, Ledjane Silva

2006-06-15

Mesoporous activated carbon has been prepared from coconut coir dust as support for adsorption of some model dye molecules from aqueous solutions. The methylene blue (MB) and remazol yellow (RY) molecules were chosen for study of the adsorption capacity of cationic and anionic dyes onto prepared activated carbon. The adsorption kinetics was studied with the Lagergren first- and pseudo-second-order kinetic models as well as the intraparticle diffusion model. The results for both dyes suggested a multimechanism sorption process. The adsorption mechanisms in the systems dyes/AC follow pseudo-second-order kinetics with a significant contribution of intraparticle diffusion. The samples simultaneously present acidic and basic sites able to act as anchoring sites for basic and acidic dyes, respectively. Calorimetric studies reveal that dyes/AC interaction forces are correlated with the pH of the solution, which can be related to the charge distribution on the AC surface. These AC samples also exhibited very short equilibrium times for the adsorption of both dyes, which is an economically favorable requisite for the activated carbon described in this work, in addition to the local abundance of the raw material.

An Inorganic Microsphere Composite for the Selective Removal of Cesium 137 from Acidic Nuclear Waste Solutions - Parts 1 and 2

DOE Office of Scientific and Technical Information (OSTI.GOV)

T. J. Tranter; T. A. Vereschchagina; V. Utgikar

2009-03-01

A new inorganic ion exchange composite for removing radioactive cesium from acidic waste streams has been developed. The new material consists of ammonium molybdophosphate, (NH4)3P(Mo3O10)4•3H2O (AMP), synthesized within hollow aluminosilicate microspheres (AMP-C), which are produced as a by-product from coal combustion. The selective cesium exchange capacity of this inorganic composite was evaluated in bench-scale column tests using simulated sodium bearing waste solution as a surrogate for the acidic tank waste currently stored at the Idaho National Laboratory (INL). Total cesium loading on the columns at saturation agreed very well with equilibrium values predicted from isotherm experiments performed previously. A numericalmore » algorithm for solving the governing partial differential equations (PDE) for cesium uptake was developed using the intraparticle mass transfer coefficient obtained from previous batch kinetic experiments. Solutions to the governing equations were generated to obtain the cesium concentration at the column effluent as a function of throughput volume using the same conditions as those used for the actual column experiments. The numerical solutions of the PDE fit the column break through data quite well for all the experimental conditions in the study. The model should therefore provide a reliable prediction of column performance at larger scales. A new inorganic ion exchange composite consisting of ammonium molybdophosphate, (NH4)3P(Mo3O10)4•3H2O (AMP), synthesized within hollow aluminosilicate microspheres (AMP-C) has been developed. Two different batches of the sorbent were produced resulting in 20% and 25% AMP loading for two and three loading cycles, respectively. The selective cesium exchange capacity of this inorganic composite was evaluated using simulated sodium bearing waste solution as a surrogate for the acidic tank waste currently stored at the Idaho National Laboratory (INL). Equilibrium isotherms obtained from these experiments were very favorable for cesium uptake and indicated maximum cesium loading of approximately 9 % by weight of dry AMP. Batch kinetic experiments were also performed to obtain the necessary data to estimate the effective diffusion coefficient for cesium in the sorbent particle. These experiments resulted in effective intraparticle cesium diffusivity coefficients of 4.99 x 10-8 cm2/min and 4.72 x 10-8 cm2/min for the 20% and 25 % AMP-C material, respectively.« less

Artificial neural network and particle swarm optimization for removal of methyl orange by gold nanoparticles loaded on activated carbon and Tamarisk.

PubMed

Ghaedi, M; Ghaedi, A M; Ansari, A; Mohammadi, F; Vafaei, A

2014-11-11

The influence of variables, namely initial dye concentration, adsorbent dosage (g), stirrer speed (rpm) and contact time (min) on the removal of methyl orange (MO) by gold nanoparticles loaded on activated carbon (Au-NP-AC) and Tamarisk were investigated using multiple linear regression (MLR) and artificial neural network (ANN) and the variables were optimized by partial swarm optimization (PSO). Comparison of the results achieved using proposed models, showed the ANN model was better than the MLR model for prediction of methyl orange removal using Au-NP-AC and Tamarisk. Using the optimal ANN model the coefficient of determination (R2) for the test data set were 0.958 and 0.989; mean squared error (MSE) values were 0.00082 and 0.0006 for Au-NP-AC and Tamarisk adsorbent, respectively. In this study a novel and green approach were reported for the synthesis of gold nanoparticle and activated carbon by Tamarisk. This material was characterized using different techniques such as SEM, TEM, XRD and BET. The usability of Au-NP-AC and activated carbon (AC) Tamarisk for the methyl orange from aqueous solutions was investigated. The effect of variables such as pH, initial dye concentration, adsorbent dosage (g) and contact time (min) on methyl orange removal were studied. Fitting the experimental equilibrium data to various isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin-Radushkevich models show the suitability and applicability of the Langmuir model. Kinetic models such as pseudo-first order, pseudo-second order, Elovich and intraparticle diffusion models indicate that the second-order equation and intraparticle diffusion models control the kinetic of the adsorption process. The small amount of proposed Au-NP-AC and activated carbon (0.015 g and 0.75 g) is applicable for successful removal of methyl orange (>98%) in short time (20 min for Au-NP-AC and 45 min for Tamarisk-AC) with high adsorption capacity 161 mg g(-1) for Au-NP-AC and 3.84 mg g(-1) for Tamarisk-AC. Copyright © 2014 Elsevier B.V. All rights reserved.

Artificial neural network and particle swarm optimization for removal of methyl orange by gold nanoparticles loaded on activated carbon and Tamarisk

NASA Astrophysics Data System (ADS)

Ghaedi, M.; Ghaedi, A. M.; Ansari, A.; Mohammadi, F.; Vafaei, A.

2014-11-01

The influence of variables, namely initial dye concentration, adsorbent dosage (g), stirrer speed (rpm) and contact time (min) on the removal of methyl orange (MO) by gold nanoparticles loaded on activated carbon (Au-NP-AC) and Tamarisk were investigated using multiple linear regression (MLR) and artificial neural network (ANN) and the variables were optimized by partial swarm optimization (PSO). Comparison of the results achieved using proposed models, showed the ANN model was better than the MLR model for prediction of methyl orange removal using Au-NP-AC and Tamarisk. Using the optimal ANN model the coefficient of determination (R2) for the test data set were 0.958 and 0.989; mean squared error (MSE) values were 0.00082 and 0.0006 for Au-NP-AC and Tamarisk adsorbent, respectively. In this study a novel and green approach were reported for the synthesis of gold nanoparticle and activated carbon by Tamarisk. This material was characterized using different techniques such as SEM, TEM, XRD and BET. The usability of Au-NP-AC and activated carbon (AC) Tamarisk for the methyl orange from aqueous solutions was investigated. The effect of variables such as pH, initial dye concentration, adsorbent dosage (g) and contact time (min) on methyl orange removal were studied. Fitting the experimental equilibrium data to various isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin-Radushkevich models show the suitability and applicability of the Langmuir model. Kinetic models such as pseudo-first order, pseudo-second order, Elovich and intraparticle diffusion models indicate that the second-order equation and intraparticle diffusion models control the kinetic of the adsorption process. The small amount of proposed Au-NP-AC and activated carbon (0.015 g and 0.75 g) is applicable for successful removal of methyl orange (>98%) in short time (20 min for Au-NP-AC and 45 min for Tamarisk-AC) with high adsorption capacity 161 mg g-1 for Au-NP-AC and 3.84 mg g-1 for Tamarisk-AC.

Adsorption of the herbicides diquat and difenzoquat on polyurethane foam: Kinetic, equilibrium and computational studies.

PubMed

Vinhal, Jonas O; Nege, Kassem K; Lage, Mateus R; de M Carneiro, José Walkimar; Lima, Claudio F; Cassella, Ricardo J

2017-11-01

This work reports a study about the adsorption of the herbicides diquat and difenzoquat from aqueous medium employing polyurethane foam (PUF) as the adsorbent and sodium dodecylsulfate (SDS) as the counter ion. The adsorption efficiency was shown to be dependent on the concentration of SDS in solution, since the formation of an ion-associate between cationic herbicides (diquat and difenzoquat) and anionic dodecylsulfate is a fundamental step of the process. A computational study was carried out to identify the possible structure of the ion-associates that are formed in solution. They are probably formed by three units of dodecylsulfate bound to one unit of diquat, and two units of dodecylsulfate bound to one unit of difenzoquat. The results obtained also showed that 95% of both herbicides present in 45mL of a solution containing 5.5mgL -1 could be retained by 300mg of PUF. The experimental data were well adjusted to the Freundlich isotherm (r 2 ≥ 0.95) and to the pseudo-second-order kinetic equation. Also, the application of Morris-Weber and Reichenberg equations indicated that an intraparticle diffusion process is active in the control of adsorption kinetics. Copyright © 2017 Elsevier Inc. All rights reserved.

Synthesis of a novel magnetic Fe3O4/γ-Al2O3 hybrid composite using electrode-alternation technique for the removal of an azo dye

NASA Astrophysics Data System (ADS)

Jung, Kyung-Won; Choi, Brian Hyun; Ahn, Kyu-Hong; Lee, Sang-Hyup

2017-11-01

A novel magnetic adsorbent of Fe3O4/γ-Al2O3 hybrid composite (denoted as M-Fe/Al-H) was developed electrochemically via a sequential application of iron and aluminum electrodes in a one-pot fashion, which called here as electrode-alternation technique, followed by pyrolysis. Physical and chemical properties of the prepared adsorbents were characterized and their feasibility towards the removal of di-anionic azo dye Acid Black 1 (AB1) was assessed. Textural and structural characterization revealed that the prepared M-Fe/Al-H possesses superior properties than those of M-Fe (sole usage of iron electrode), which may improve the adsorption capacity. Kinetics revealed that the adsorption equilibrium was reached within 12 h with approximately 90% of the equilibrium adsorption capacity within the first 3 h. Comprehensive analysis using the pseudo-second order and intraparticle diffusion models indicated that the dominant mechanism of the reaction is film diffusion with intraparticle diffusion being the rate determining step. The adsorption equilibrium isotherm data were best represented by the Sips isotherm model, which found to be approximately 1501, 1786, and 1959 mg/g at 283, 293, and 303 K, respectively. The exceptional performance as well as its ease of separation allows M-Fe/Al-H to be a promising candidate as an effective for azo dye removal from various aqueous medium.

Effect of electrolyte nature on kinetics of remazol yellow G removal by electrocoagulation

NASA Astrophysics Data System (ADS)

Rajabi, M.; Bagheri-Roochi, M.; Asghari, A.

2011-10-01

The present study describes an electrocoagulation process for the removal of remazol yellow G from dye solutions using Iron as the anode and Steel as the cathode. Pseudo-first-order, pseudo-second-order and intraparticle diffusion models were used to analyze the kinetic data obtained at different concentrations in different conditions. The adsorption kinetics was well described by the pseudo-second-order kinetic model.

Removal of methyl violet 2B dye from aqueous solution using Nepenthes rafflesiana pitcher and leaves

NASA Astrophysics Data System (ADS)

Kooh, Muhammad Raziq Rahimi; Dahri, Muhammad Khairud; Lim, Linda B. L.

2017-11-01

This study reported Nepenthes rafflesiana pitcher (NP) and Nepenthes rafflesiana leaves (NL) as new adsorbents for methyl violet (MV) dye. The experiments were done using 2 h contact time and without any pH alteration (pH 4.4). The effects of pH and ionic strength revealed hydrophobic-hydrophobic interaction as the predominant force of dye interaction with the adsorbent. Both NP-MV and NL-MV followed pseudo-second-order model indicating the adsorption processes may be governed by chemical process. Weber-Morris intraparticle diffusion model verified that the rate-limiting step of both the NP-MV and NL-MV systems is not intraparticle diffusion. The Langmuir model best described the adsorption process with high maximum monolayer adsorption ( q m) of 288.7 and 194.0 mg g-1 for NP-MV and NL-MV, respectively. Thermodynamics studies revealed both NP-MV and NL-MV systems are spontaneous and endothermic in nature. From the regeneration study, it was found that NP's and NL's adsorption capacities could be recovered using distilled water and base whereby distilled water was able to recover 78% (NP) and 71% (NL) while base was able to recover 82% for both samples after three regeneration cycles.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anggita, R. K. Wardani, E-mail: anggita14@mhs.chem.its.ac.id; Yuniar, V. T. P., E-mail: yuniar11@mhs.chem.its.ac.id; Aini, W. T., E-mail: aini11@mhs.chem.its.ac.id

In this study, the influence of hydrothermal temperature and time at zeolite X supported on glasswool were investigated. The results of characterization using XRD showed that a single phase zeolite X with highest crystallinity was obtained when hydrothermal temperature and time at 100°C during 24 hours (ZXF100-24H). The CO{sub 2} adsorption capacity of ZXF100-24H has reached up to 10.15 wt. %. Kinetics of CO{sub 2} adsorption onto zeolite X supported on glasswool was investigated using pseudo-first-order, pseudo-second-order and intra-particle diffusion kinetic models. After evaluating three kinetic models for CO{sub 2} adsorption at adsorption temperatures of 30°C, 40°C and 50°C, itmore » was found that intra-particle diffusion kinetic model provided the best fitting for the adsorption data. Furthermore, the thermodynamic parameters of CO{sub 2} adsorption were obtained as follows, Gibbs free energy change (ΔG°) are −0.409 kJ/mol at 30°C, −0.274 kJ/mol at 40°C and −0.138 kJ/mol at 50 °C, whereas the enthalpy change (ΔH°) is −4.53 kJ/mol and the entropy change (ΔS°) is −0.0135 kJ/(mol K).« less

Impact of biochar produced from post-harvest residue on the adsorption behavior of diesel oil on loess soil.

PubMed

Jiang, Yu Feng; Sun, Hang; Yves, Uwamungu J; Li, Hong; Hu, Xue Fei

2016-02-01

The primary objective of this study was to investigate the effect of biochar, produced from wheat residue at different temperatures, on the adsorption of diesel oil by loess soil. Kinetic and equilibrium data were processed to understand the adsorption mechanism of diesel by biochar-affected loess soil; dynamic and thermodynamic adsorption experiments were conducted to characterize this adsorption. The surface features and chemical structure of biochar, modified at varying pyrolytic temperatures, were investigated using surface scanning electron microscopy and Fourier transform infrared analysis. The kinetic data showed that the adsorption of diesel oil onto loess soil could be described by a pseudo-second-order kinetic model, with the rate-controlling step being intraparticle diffusion. However, in the presence of biochar, boundary layer control and intraparticle diffusion were both involved in the adsorption. Besides, the adsorption equilibrium data were well described by the Freundlich isothermal model. The saturated adsorption capacity weakened as temperature increased, suggesting a spontaneous exothermic process. Thermodynamic parameter analysis showed that adsorption was mainly a physical process and was enhanced by chemical adsorption. The adsorption capacity of loess soil for diesel oil was weakened with increasing pH. The biochar produced by pyrolytic wheat residue increased the adsorption behavior of petroleum pollutants in loess soil.

Effect of Humic Acid on As Redox Transformation and Kinetic Adsorption onto Iron Oxide Based Adsorbent (IBA)

PubMed Central

Fakour, Hoda; Lin, Tsair-Fuh

2014-01-01

Due to the importance of adsorption kinetics and redox transformation of arsenic (As) during the adsorption process, the present study elucidated natural organic matter (NOM) effects on As adsorption-desorption kinetics and speciation transformation. The experimental procedures were conducted by examining interactions of arsenate and arsenite with different concentrations of humic acid (HA) as a model representative of NOM, in the presence of iron oxide based adsorbent (IBA), as a model solid surface in three environmentally relevant conditions, including the simultaneous adsorption of both As and HA onto IBA, HA adsorption onto As-presorbed IBA, and As adsorption onto HA-presorbed IBA. Experimental adsorption-desorption data were all fitted by original and modified Lagergren pseudo-first and -second order adsorption kinetic models, respectively. Weber’s intraparticle diffusion was also used to gain insight into the mechanisms and rate controlling steps, which the results suggested that intraparticle diffusion of As species onto IBA is the main rate-controlling step. Different concentrations of HA mediated the redox transformation of As species, with a higher oxidation ability than reduction. The overall results indicated the significant effect of organic matter on the adsorption kinetics and redox transformation of As species, and consequently, the fate, transport and mobility of As in different environmentally relevant conditions. PMID:25325357

Kinetics and Mechanisms of Phosphorus Adsorption in Soils from Diverse Ecological Zones in the Source Area of a Drinking-Water Reservoir

PubMed Central

Zhang, Liang; Loáiciga, Hugo A.; Xu, Meng; Du, Chao; Du, Yun

2015-01-01

On-site soils are increasingly used in the treatment and restoration of ecosystems to harmonize with the local landscape and minimize costs. Eight natural soils from diverse ecological zones in the source area of a drinking-water reservoir in central China are used as adsorbents for the uptake of phosphorus from aqueous solutions. The X-ray fluorescence (XRF) spectrometric and BET (Brunauer-Emmett-Teller) tests and the Scanning Electron Microscopy (SEM) and Fourier Transform Infrared (FTIR) spectral analyses are carried out to investigate the soils’ chemical properties and their potential changes with adsorbed phosphorous from aqueous solutions. The intra-particle diffusion, pseudo-first-order, and pseudo-second-order kinetic models describe the adsorption kinetic processes. Our results indicate that the adsorption processes of phosphorus in soils occurred in three stages and that the rate-controlling steps are not solely dependent on intra-particle diffusion. A quantitative comparison of two kinetics models based on their linear and non-linear representations, and using the chi-square (χ2) test and the coefficient of determination (r2), indicates that the adsorptive properties of the soils are best described by the non-linear pseudo-second-order kinetic model. The adsorption characteristics of aqueous phosphorous are determined along with the essential kinetic parameters. PMID:26569278

Elucidation of the naproxen sodium adsorption onto activated carbon prepared from waste apricot: kinetic, equilibrium and thermodynamic characterization.

PubMed

Onal, Y; Akmil-Başar, C; Sarici-Ozdemir, C

2007-09-30

In this study, activated carbon (WA11Zn5) was prepared from waste apricot, which is waste in apricot plants in Malatya, by chemical activation with ZnCl(2). BET surface area of activated carbon is determined as 1060 m(2)/g. The ability of WA11Zn5, to remove naproxen sodium from effluent solutions by adsorption has been studied. Equilibrium isotherms for the adsorption of naproxen sodium on activated carbon were measured experimentally. Results were analyzed by the Langmiur, Freundlich equation using linearized correlation coefficient at 298 K. The characteristic parameters for each isotherm have been determined. Langmiur equation is found to best represent the equilibrium data for naproxen sodium-WA11Zn5 systems. The monolayer adsorption capacity of WA11Zn5 for naproxen sodium was found to be 106.38 mg/g at 298 K. The process was favorable and spontaneous. The kinetics of adsorption of naproxen sodium have been discussed using three kinetic models, i.e., the pseudo first-order model, the pseudo second-order model, the intraparticle diffusion model. Kinetic parameters and correlation coefficients were determined. It was shown that the pseudo second-order kinetic equation could describe the adsorption kinetics for naproxen sodium onto WA11Zn5. The thermodynamic parameters, such as DeltaG degrees , DeltaS degrees and DeltaH degrees, were calculated. The thermodynamics of naproxen sodium-WA11Zn5 system indicates endothermic process.

Removal of humic acid from aqueous solution using dual PMMA/PVDF composite nanofiber: kinetics study

NASA Astrophysics Data System (ADS)

Zulfikar, M. A.; Afrianingsih, I.; Bahri, A.; Nasir, M.; Alni, A.; Setiyanto, H.

2018-05-01

The removal of humic acid from aqueous solution using dual poly(methyl methacrylate)/polyvinyl difluoride composite nanofiber under the influence of concentration has been studied. The experiments were performed using humic acid (HA) as an adsorbate at concentration in the range of 50-200 mg/L. Pseudo-first-order, pseudo-second-order, and intra-particle diffusion models were used to describe the kinetic data and the rate constants were evaluated. It was observed that the amount of humic acid removed decrease with increasing concentration. The kinetic study revealed that pseudo-second order model fitted well the kinetic data, while the external diffusion or boundary layer diffusion was the main rate determining step in the removal process.

Effects of low molecular weight organic acids on (137)Cs release from contaminated soils.

PubMed

Chiang, Po Neng; Wang, Ming Kuang; Huang, Pan Ming; Wang, Jeng Jong

2011-06-01

Radio pollutant removal is one of several priority restoration strategies for the environment. This study assessed the effect of low molecular weight organic acid on the lability and mechanisms for release of (137)Cs from contaminated soils. The amount of (137)Cs radioactivity released from contaminated soils reacting with 0.02 M low molecular weight organic acids (LMWOAs) specifically acetic, succinic, oxalic, tartaric, and citric acid over 48 h were 265, 370, 760, 850, and 1002 Bq kg(-1), respectively. The kinetic results indicate that (137)Cs exhibits a two-step parabolic diffusion equation and a good linear relationship, indicating that the parabolic diffusion equation describes the data quite well, as shown by low p and high r(2) values. The fast stage, which was found to occur within a short period of time (0.083-3 h), corresponds to the interaction of LMWOAs with the surface of clay minerals; meanwhile, during the slow stage, which occurs over a much longer time period (3-24 h), desorption primarily is attributed to inter-particle or intra-particle diffusion. After a fifth renewal of the LMWOAs, the total levels of (137)Cs radioactivity released by acetic, succinic, oxalic, tartaric, and citric acid were equivalent to 390, 520, 3949, 2061, and 4422 Bq kg(-1) soil, respectively. H(+) can protonate the hydroxyl groups and oxygen atoms at the broken edges or surfaces of the minerals, thereby weakening Fe-O and Al-O bonds. After protonation of H(+), organic ligands can attack the OH and OH(2) groups in the minerals easily, to form complexes with surface structure cations, such as Al and Fe. The amounts of (137)Cs released from contaminated soil treated with LMWOAs were substantially increased, indicating that the LMWOAs excreted by the roots of plants play a critical role in (137)Cs release. Copyright © 2011 Elsevier Ltd. All rights reserved.

Sorption of lead from aqueous solution by chemically modified carbon adsorbents.

PubMed

Nadeem, Muhammad; Mahmood, A; Shahid, S A; Shah, S S; Khalid, A M; McKay, G

2006-12-01

An indigenously prepared, steam activated and chemically modified carbon from husk and pods of Moringa oleifera (M. oleifera), an agricultural waste, was comparatively examined as an adsorbent for the removal of lead from aqueous solutions. Studies were conducted as a function of contact time, initial metal concentration, dose of adsorbent, agitation speed, particle size and pH. Maximum uptake capacities were found to be, 98.89, 96.58, 91.8, 88.63, 79.43% for cetyltrimethyl ammonium bromide (CTAB), phosphoric, sulfuric, hydrochloric acid treated and untreated carbon adsorbents, respectively. Bangham, pseudo-first- and second-order, intra-particle diffusion equations were implemented to express the sorption mechanism by utilized adsorbents. Adsorption rate of lead ions was found to be considerably faster for chemically modified adsorbents than unmodified. The results of adsorption were fitted to both the Langmuir and Freundlich models. Satisfactory agreement between the metal uptake capacities by the adsorbents at different time intervals was expressed by the correlation coefficient (R(2)). The Langmuir model represented the sorption process better than the Freundlich one, with R(2) values ranging from 0.994 to 0.998.

Adsorption isotherms and kinetics studies of malachite green on chitin hydrogels.

PubMed

Tang, Hu; Zhou, Weijie; Zhang, Lina

2012-03-30

A chitin hydrogel with concentration 3 wt% (CG3) was successfully prepared from chitin solution dissolved in 8 wt% NaOH/4 wt% urea aqueous system at low temperature by crosslinking with 5 wt% epichlorohydrin. The experimental results revealed that CG3 exhibited high efficiency to remove dye (malachite green) from aqueous solution, as a result of their microporous structure, large surface area and affinity on the dye. The equilibrium process was described well by the Langmuir isotherm model, showing a monolayer adsorption. From kinetic experiments, the adsorption process followed the pseudo-second-order kinetic model, indicating that the overall rate of dye uptake could be controlled by external mass transfer at the beginning of adsorption, while intraparticle diffusion controlled the overall rate of adsorption at a later stage. The activation energy calculated from Arrhenius equation and the result of SEM and FTIR indicated that the adsorption of malachite green on the CG3 was physical process. This work provided an attractive adsorbent for removing of the hazardous materials from wastewater. Crown Copyright © 2012. Published by Elsevier B.V. All rights reserved.

Adsorption Behavior of Ferromagnetic Carbon Nanotubes for Methyl Orange from Aqueous Solution.

PubMed

Wang, Liping; Zhang, Mingyu; Zhao, Chenxi; Yang, Shan

2016-03-01

The ferromagnetic carbon nanotubes which can be easily separated from aqueous solution were prepared and characterized by scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction (XRD). Batch experiments were carried out to investigate the adsorption behavior of ferromagnetic carbon nanotubes for removing methyl orange (MO). The results showed that these ferromagnetic carbon nanotubes were richer in surface function groups than the carbon nanotubes did, furthermore, both γ-Fe2O3 and Fe with ferromagnetism were found on the surface of carbon nanotubes. The results also demonstrated that ferromagnetic carbon nanotubes possessed stronger adsorption ability for MO than carbon nanotubes did. The adsorption isotherms followed Langmuir isotherm equation and the adsorption kinetics could be well described with the pseudo second-order kinetic model. The adsorption process involved an intraparticle diffusion, while it was not the only rate-controlling step. The values of AG were negative and the value of ΔH is -12.37 kJ/mol, proving that the adsorption of MO onto ferromagnetic carbon nanotubes was a spontaneous and exothermic process.

Preparation of steam activated carbon from rubberwood sawdust (Hevea brasiliensis) and its adsorption kinetics.

PubMed

Prakash Kumar, B G; Shivakamy, K; Miranda, Lima Rose; Velan, M

2006-08-25

Activated carbon was produced from a biowaste product, rubberwood sawdust (RWSD) using steam in a high temperature fluidized bed reactor. Experiments were carried out to investigate the influence of various process parameters such as activation time, activation temperature, particle size and fluidising velocity on the quality of the activated carbon. The activated carbon was characterized based on its iodine number, methylene blue number, Brauner Emmet Teller (BET) surface area and surface area obtained using the ethylene glycol mono ethyl ether (EGME) retention method. The best quality activated carbon was obtained at an activation time and temperature of 1h and 750 degrees C for an average particle size of 0.46 mm. The adsorption kinetics shows that pseudo-second-order rate fitted the adsorption kinetics better than pseudo-first-order rate equation. The adsorption capacity of carbon produced from RWSD was found to be 1250 mg g(-1) for the Bismark Brown dye. The rate constant and diffusion coefficient for intraparticle transport were determined for steam activated carbon. The characteristic of the prepared activated carbon was found comparable to the commercial activated carbon.

Adsorption of Zinc(II) on diatomite and manganese-oxide-modified diatomite: a kinetic and equilibrium study.

PubMed

Caliskan, Necla; Kul, Ali Riza; Alkan, Salih; Sogut, Eda Gokirmak; Alacabey, Ihsan

2011-10-15

The removal of Zn(II) ions from aqueous solution was studied using natural and MnO(2) modified diatomite samples at different temperatures. The linear Langmuir, Freundlich and Dubinin-Radushkevich (D-R) adsorption equations were applied to describe the equilibrium isotherms. From the D-R model, the mean adsorption energy was calculated as >8 kJ mol(-1), indicating that the adsorption of Zn(II) onto diatomite and Mn-diatomite was physically carried out. In addition, the pseudo-first-order, pseudo-second-order and intraparticle diffusion models were used to determine the kinetic data. The experimental data were well fitted by the pseudo-second-order kinetic model. Thermodynamic parameters such as the enthalpy (ΔH(0)), Gibbs' free energy (ΔG(0)) and entropy (ΔS(0)) were calculated for natural and MnO(2) modified diatomite. These values showed that the adsorption of Zn(II) ions onto diatomite samples was controlled by a physical mechanism and occurred spontaneously. Copyright © 2011 Elsevier B.V. All rights reserved.

Removal of acid blue 062 on aqueous solution using calcinated colemanite ore waste.

PubMed

Atar, Necip; Olgun, Asim

2007-07-19

Colemanite ore waste (CW) has been employed as adsorbent for the removal of acid blue 062 anionic dye (AB 062) from aqueous solution. The adsorption of AB 062 onto CW was examined with respect to contact time, calcination temperature, particle size, pH, adsorbent dosage and temperature. The physical and chemical properties of the CW, such as particle sizes and calcinations temperature, play important roles in dye adsorption. The dye adsorption largely depends on the initial pH of the solution with maximum uptake occurring at pH 1. Three simplified kinetics models, namely, pseudo-first order, pseudo-second order, and intraparticle diffusion models were tested to investigate the adsorption mechanisms. The kinetic adsorption of AB 062 on CW follows a pseudo-second order equation. The adsorption data have been analyzed using Langmuir and Freundlich isotherms. The results indicate that the Langmuir model provides the best correlation of the experimental data. Isotherms have also been used to obtain the thermodynamic parameters such as free energy, enthalpy and entropy of the adsorption of dye onto CW.

Remediation of anionic dye from aqueous system using bio-adsorbent prepared by microwave activation.

PubMed

Sharma, Arush; Sharma, Gaurav; Naushad, Mu; Ghfar, Ayman A; Pathania, Deepak

2018-04-01

The present study was attempted to ascertain the possible application of activated carbon as a cost-effective and eco-friendly adsorbent prepared via microwave-assisted chemical activation. The activated carbon was characterized using different techniques. The various adsorption parameters have been optimized to examine the viability of activated carbon as a plausible sorbent for the remediation of Congo red (CR) dye from the aquatic system. The equilibrium data adequately fitted to the Langmuir isotherm with better R 2 (0.994). The maximum adsorption capacity (q m ) of activated carbon was recorded to be 68.96 mg/g. Additionally, sorptional kinetic data were examined by reaction-based and diffusion-based models such as pseudo-first-order and pseudo-second-order equations, and Elovich, intra-particle diffusion, and Dumwald-Wagner models, respectively. The computed values of thermodynamic parameters such as free energy change (ΔG 0 ), enthalpy change (ΔH 0 ) and entropy change (ΔS 0 ) were recorded as -3.63, 42.47 and 152.07 J/mol K, respectively, at 30°C, which accounted for a favorable, spontaneous and endothermic process. The regeneration study emphasized that the percentage uptake declined from 90.35% to 83.45% after six cycles of testing. So, our findings implied that activated carbon produced from biomass must be cost-effectively used as an adsorbent for detoxifying the CR dye from industrial effluents.

Nonequilibrium electrokinetic effects in beds of ion-permselective particles.

PubMed

Leinweber, Felix C; Tallarek, Ulrich

2004-12-21

Electrokinetic transport of fluorescent tracer molecules in a bed of porous glass beads was investigated by confocal laser scanning microscopy. Refractive index matching between beads and the saturating fluid enabled a quantitative analysis of intraparticle and extraparticle fluid-side concentration profiles. Kinetic data were acquired for the uptake and release of electroneutral and counterionic tracer under devised conditions with respect to constant pressure-driven flow through the device and the effect of superimposed electrical fields. Transport of neutral tracer is controlled by intraparticle mass transfer resistance which can be strongly reduced by electroosmotic flow, while steady-state distributions and bead-averaged concentrations are unaffected by the externally applied fields. Electrolytes of low ionic strength caused the transport through the charged (mesoporous) beads to become highly ion-permselective, and concentration polarization is induced in the bulk solution due to the superimposed fields. The depleted concentration polarization zone comprises extraparticle fluid-side mass transfer resistance. Ionic concentrations in this diffusion boundary layer decrease at increasing field strength, and the flux densities approach an upper limit. Meanwhile, intraparticle transport of counterions by electromigration and electroosmosis continues to increase and finally exceeds the transport from bulk solution into the beads. A nonequilibrium electrical double layer is induced which consists of mobile and immobile space charge regions in the extraparticle bulk solution and inside a bead, respectively. These electrical field-induced space charges form the basis for nonequilibrium electrokinetic phenomena. Caused by the underlying transport discrimination (intraparticle electrokinetic vs extraparticle boundary-layer mass transfer), the dynamic adsorption capacity for counterions can be drastically reduced. Further, the extraparticle mobile space charge region leads to nonlinear electroosmosis. Flow patterns can become highly chaotic, and electrokinetic instability mixing is shown to increase lateral dispersion. Under these conditions, the overall axial dispersion of counterionic tracer can be reduced by more than 2 orders of magnitude, as demonstrated by pulse injections.

The surface characteristics of hyperbranched polyamide modified corncob and its adsorption property for Cr(VI)

NASA Astrophysics Data System (ADS)

Lin, Hai; Han, Shaoke; Dong, Yingbo; He, Yinhai

2017-08-01

A low-cost anion adsorbent for Cr(VI) effectively removing was synthesized by hyperbranched polyamide modified corncob (HPMC). Samples were characterized by Brunauer-Emmett-Teller (BET) surface area analysis, field-emission scanning electron microscopy (FE-SEM) with energy-dispersive X-ray spectroscopy, Fourier transform infrared (FTIR) and zeta potential analysis. Kinetics, isotherms and thermodynamics studies of HPMC for Cr(VI) adsorption were investigated in batch static experiments, in the temperature range of 25-45 °C, pH = 2.0. Results showed that the adsorption was rapid and stable, with the uptake capacity higher than 80% after 30 min. Adsorption behavior and rate-controlling mechanisms were analyzed using three kinetic models (pseudo-first order, pseudo-second order, intra-particle kinetic model). Kinetic studies showed that the adsorption of HPMC to Cr(VI) relied the pseudo-second-order model, and controlled both by the intra-particle diffusion and film diffusion. Equilibrium data was tested by Langmuir and Freundlich adsorption isotherm models. Langmuir model was more suitable to indicate a homogeneous distribution of active sites on HPMC and monolayer adsorption. The maximum adsorption capacity from the Langmuir model, qmax, was 131.6 mg/g at pH 2.0 and 45 °C for HPMC. Thermodynamic parameters revealed spontaneous and endothermic nature of the Cr(VI) adsorption onto HPMC.

Effect of aniline on cadmium adsorption by sulfanilic acid-grafted magnetic graphene oxide sheets.

PubMed

Hu, Xin-jiang; Liu, Yun-guo; Zeng, Guang-ming; Wang, Hui; Hu, Xi; Chen, An-wei; Wang, Ya-qin; Guo, Yi-Mming; Li, Ting-ting; Zhou, Lu; Liu, Shao-heng; Zeng, Xiao-xia

2014-07-15

Cd(II) has posed severe health risks worldwide. To remove this contaminant from aqueous solution, the sulfanilic acid-grafted magnetic graphene oxide sheets (MGOs/SA) were prepared and characterized. The mutual effects of Cd(II) and aniline adsorption on MGOs/SA were studied. The effects of operating parameters such as pH, ionic strength, contact time and temperature on the Cd(II) enrichment, as well as the adsorption kinetics and isotherm were also investigated. The results demonstrated that MGOs/SA could effectively remove Cd(II) and aniline from the aqueous solution and the two adsorption processes were strongly dependent on solution pH. The Cd(II) adsorption was reduced by the presence of aniline at pH<5.4 but was improved at pH>5.4. The presence of Cd(II) diminished the adsorption capacity for aniline at pH<7.8 but enhanced the aniline adsorption at pH>7.8. The decontamination of Cd(II) by MGOs/SA was influenced by ionic strength. Besides, the adsorption process could be well described by pseudo-second-order kinetic model. The intraparticle diffusion study revealed that the intraparticle diffusion was not the only rate-limiting step for the adsorption process. Moreover, the experimental data of isotherm followed the Freundlich isotherm model. Copyright © 2014 Elsevier Inc. All rights reserved.

Preparation of low cost activated carbon from Myrtus communis and pomegranate and their efficient application for removal of Congo red from aqueous solution

NASA Astrophysics Data System (ADS)

Ghaedi, Mehrorang; Tavallali, Hossein; Sharifi, Mahdi; Kokhdan, Syamak Nasiri; Asghari, Alireza

2012-02-01

In this research, the potential applicability of activated carbon prepared from Myrtus communis (AC-MC) and pomegranate (AC-PG) as useful adsorbents for the removal of Congo red (CR) from aqueous solutions in batch method was investigated. The effects of pH, contact time, agitation time and amount of adsorbents on removal percentage of Congo red on both adsorbents were examined. Increase in pH up to 6 for AC-MC and pH 7 for AC-PG increase the adsorption percentage (capacity) and reach equilibrium within 30 min of contact time. Fitting the experimental data to conventional isotherm models like Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich show that the experimental data fitted very well to the Freundlich isotherm for AC-MC and Langmuir isotherm for AC-PG. Fitting the experimental data to different kinetic models such as pseudo first-order, pseudo second-order, Elovich and intraparticle diffusion mechanism showed the applicability of a pseudo second-order with involvement of intraparticle diffusion model for interpretation of experimental data for both adsorbents. The adsorption capacity of AC-PG and AC-MC for the removal of CR was found to be 19.231 and 10 mg g -1. These results clearly indicate the efficiency of adsorbents as a low cost adsorbent for treatment of wastewater containing CR.

Low cost biosorbent "banana peel" for the removal of phenolic compounds from olive mill wastewater: kinetic and equilibrium studies.

PubMed

Achak, M; Hafidi, A; Ouazzani, N; Sayadi, S; Mandi, L

2009-07-15

The aim of this work is to determine the potential of application of banana peel as a biosorbent for removing phenolic compounds from olive mill wastewaters. The effect of adsorbent dosage, pH and contact time were investigated. The results showed that the increase in the banana peel dosage from 10 to 30 g/L significantly increased the phenolic compounds adsorption rates from 60 to 88%. Increase in the pH to above neutrality resulted in the increase in the phenolic compounds adsorption capacity. The adsorption process was fast, and it reached equilibrium in 3-h contact time. The Freundlich and Langmuir adsorption models were used for mathematical description of the adsorption equilibrium and it was found that experimental data fitted very well to both Freundlich and Langmuir models. Batch adsorption models, based on the assumption of the pseudo-first-order, pseudo-second-order and intraparticle diffusion mechanism, showed that kinetic data follow closely the pseudo-second-order than the pseudo-first-order and intraparticle diffusion. Desorption studies showed that low pH value was efficient for desorption of phenolic compounds. These results indicate clearly the efficiency of banana peel as a low-cost solution for olive mill wastewaters treatment and give some preliminary elements for the comprehension of the interactions between banana peel as a bioadsorbent and the very polluting compounds from the olive oil industry.

Preparation of low cost activated carbon from Myrtus communis and pomegranate and their efficient application for removal of Congo red from aqueous solution.

PubMed

Ghaedi, Mehrorang; Tavallali, Hossein; Sharifi, Mahdi; Kokhdan, Syamak Nasiri; Asghari, Alireza

2012-02-01

In this research, the potential applicability of activated carbon prepared from Myrtus communis (AC-MC) and pomegranate (AC-PG) as useful adsorbents for the removal of Congo red (CR) from aqueous solutions in batch method was investigated. The effects of pH, contact time, agitation time and amount of adsorbents on removal percentage of Congo red on both adsorbents were examined. Increase in pH up to 6 for AC-MC and pH 7 for AC-PG increase the adsorption percentage (capacity) and reach equilibrium within 30 min of contact time. Fitting the experimental data to conventional isotherm models like Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich show that the experimental data fitted very well to the Freundlich isotherm for AC-MC and Langmuir isotherm for AC-PG. Fitting the experimental data to different kinetic models such as pseudo first-order, pseudo second-order, Elovich and intraparticle diffusion mechanism showed the applicability of a pseudo second-order with involvement of intraparticle diffusion model for interpretation of experimental data for both adsorbents. The adsorption capacity of AC-PG and AC-MC for the removal of CR was found to be 19.231 and 10 mg g(-1). These results clearly indicate the efficiency of adsorbents as a low cost adsorbent for treatment of wastewater containing CR. Copyright © 2011 Elsevier B.V. All rights reserved.

Study of sorption-retarded U(VI) diffusion in Hanford silt/clay material.

PubMed

Bai, Jing; Liu, Chongxuan; Ball, William P

2009-10-15

A diffusion cell method was applied to measure the effective pore diffusion coefficient (Dp) for U(VI) under strictly controlled chemical conditions in a silt/clay sediment from the U.S. Department of Energy Hanford site, WA. "Inward-flux" diffusion studies were conducted in which [U(VI)] in both aqueous and solid phases was measured as a function of distance in the diffusion cell under conditions of constant concentration at the cell boundaries. A sequential extraction method was developed to measure sorbed contaminant U(VI) in the solid phase containing extractable background U(VI). The effect of sorption kinetics on U(VI) interparticle diffusion was evaluated by comparing sorption-retarded diffusion models with sorption described either as equilibrium or intraparticle diffusion-limited processes. Both experimental and modeling results indicated that (1) a single pore diffusion coefficient can simulate the diffusion of total aqueous U(VI), and (2) the local equilibrium assumption (LEA) is appropriate for modeling sorption-retarded diffusion under the given experimental conditions. Dp of 1.6-1.7 x 10(-6) cm2/s was estimated in aqueous solution at pH 8.0 and saturated with respect to calcite, as relevant to some subsurface regions of the Hanford site.

Comparison of adsorption of Remazol Black B and Acidol Red on microporous activated carbon felt.

PubMed

Donnaperna, L; Duclaux, L; Gadiou, R; Hirn, M-P; Merli, C; Pietrelli, L

2009-11-15

The adsorption of two anionic dyes, Remazol Black B (RB5) and Acidol Red 2BE-NW (AR42), onto a microporous activated carbon felt was investigated. The characterization of carbon surface chemistry by X-ray microanalysis, Boehm titrations, and pH-PZC measurements indicates that the surface oxygenated groups are mainly acidic. The rate of adsorption depends on the pH and the experimental data fit the intraparticle diffusion model. The pore size distribution obtained by DFT analysis shows that the mean pore size is close to 1nm, which indicates that a slow intraparticle diffusion process control the adsorption. The adsorption isotherms were measured for different pH values. The Khan and the Langmuir-Freundlich models lead to the best agreement with experimental data for RB5 and AR42, respectively. These isotherm simulations and the pH dependence of adsorption show that the adsorption capacity is mainly controlled by nondispersive electrostatic interactions for pH values below 4. The adsorption kinetics, the irreversibility of the process, and the influence of the pH indicate that the rate of adsorption in this microporous felt proceeds through two steps. The first one is fast and results from direct interaction of dye molecules with the external surface of the carbon material (which account for 10% of the whole surface area); in the second, slow step, the adsorption rate is controlled by the slow diffusion of dye molecules into the narrow micropores. The influence of temperature on the adsorption isotherms was studied and the thermodynamic parameters were obtained. They show that the process is spontaneous and exothermic.

[Removal Kinetics and Mechanism of Aniline by Manganese-oxide-modified Diatomite].

PubMed

Xiao, Shao-dan; Liu, Lu; Jiang, Li-ying; Chen, Jian-meng

2015-06-01

A novel rapid green one-step method was developed for the preparation of manganese modified diatomite (Mn-D) by treating roasted diatomite with an acidic permanganate solution. The effects of calcination temperature and mass ratio of KMnO4 and diatomite (p) on aniline removal efficiency of Mn-D were investigated. The removal kinetics and mechanism of aniline by Mn-D were also discussed. The results showed that when the optimal calcination temperature was 450 degrees C, p was 1.6, and the loading amounts of δ-MnO2 was 0.82 g x g(-1), Mn-D had a great performance for aniline removal, and more than 80% of aniline was adsorbed within 10 minutes, accompanied with the release of Mn2+. In acidic conditions, the adsorption process on Mn-D followed pseudo-second-order and was mainly controlled by intra-particle diffusion. The best fitting of the experimental adsorption data was given by the Freundlich equation. Gas chromatograph-mass spectrometer was applied to identify the reaction intermediates at different times, and azobenzene was found to be the main reaction intermediate in the degradation system. Based on the above observations, the possible degradation pathway of aniline by Mn-D was proposed.

[Bromate reduction by granular activated carbon].

PubMed

Huang, Xin; Gao, Nai-yun; Lu, Pin-pin

2007-10-01

Batch experiments were conducted to evaluate the kinetics of reducing bromate to bromide by granular activated carbon. Solution conditions were studied in details, such as pH, ionic strength, temperature and initial bromate concentration. The results showed the removal capacity of GAC was positively relevant to surface basic functional groups. The whole process was inhibited by other anions in solution and the inhibition sequence was NO3(-) > SO4(2-) > Cl(-). Pseudo-second order rate equation and intraparticle diffusion model were applied to fit the process of bromate reduction and the process of bromide formation, respectively, with regression coefficients higher than 0.97 at most cases. Bromate removal was found to be favored under conditions with low pH value and low ionic strength. Both sorption rate of bromate and formation rate of bromide were decreased, and then increased along with the increase of temperature during 15-42 degree C. In this experiment, the maximum adsorption capacity of GAC is 769.23 micromol/g (98.4 mg/g), whereas the sorption process is slow and easily influenced. It is concluded that the sorption of bromate by the micropore portion of GAC was influenced by the release of bromide.

Optimization of the ultrasonic assisted removal of methylene blue by gold nanoparticles loaded on activated carbon using experimental design methodology.

PubMed

Roosta, M; Ghaedi, M; Daneshfar, A; Sahraei, R; Asghari, A

2014-01-01

The present study was focused on the removal of methylene blue (MB) from aqueous solution by ultrasound-assisted adsorption onto the gold nanoparticles loaded on activated carbon (Au-NP-AC). This nanomaterial was characterized using different techniques such as SEM, XRD, and BET. The effects of variables such as pH, initial dye concentration, adsorbent dosage (g), temperature and sonication time (min) on MB removal were studied and using central composite design (CCD) and the optimum experimental conditions were found with desirability function (DF) combined response surface methodology (RSM). Fitting the experimental equilibrium data to various isotherm models such as Langmuir, Freundlich, Tempkin and Dubinin-Radushkevich models show the suitability and applicability of the Langmuir model. Analysis of experimental adsorption data to various kinetic models such as pseudo-first and second order, Elovich and intraparticle diffusion models show the applicability of the second-order equation model. The small amount of proposed adsorbent (0.01 g) is applicable for successful removal of MB (RE>95%) in short time (1.6 min) with high adsorption capacity (104-185 mg g(-1)). Copyright © 2013 Elsevier B.V. All rights reserved.

Intraparticle reduction of arsenite (As(III)) by nanoscale zerovalent iron (nZVI) investigated with In Situ X-ray absorption spectroscopy.

PubMed

Yan, Weile; Vasic, Relja; Frenkel, Anatoly I; Koel, Bruce E

2012-07-03

While a high efficiency of contaminant removal by nanoscale zerovalent iron (nZVI) has often been reported for several contaminants of great concern, including aqueous arsenic species, the transformations and translocation of contaminants at and within the nanoparticles are not clearly understood. By analysis using in situ time-dependent X-ray absorption spectroscopy (XAS) of the arsenic core level for nZVI in anoxic As(III) solutions, we have observed that As(III) species underwent two stages of transformation upon adsorption at the nZVI surface. The first stage corresponds to breaking of As-O bonds at the particle surface, and the second stage involves further reduction and diffusion of arsenic across the thin oxide layer enclosing the nanoparticles, which results in arsenic forming an intermetallic phase with the Fe(0) core. Extended X-ray absorption fine-structure (EXAFS) data from experiments conducted at different iron/arsenic ratios indicate that the reduced arsenic species tend to be enriched at the surface of the Fe(0) core region and had limited mobility into the interior of the metal core within the experimental time frame (up to 22 h). Therefore, there was an accumulation of partially reduced arsenic at the Fe(0)/oxide interface when a relatively large arsenic content was present in the solid phase. These results illuminate the role of intraparticle diffusion and reduction in affecting the chemical state and spatial distribution of arsenic in nZVI materials.

Effect of biochar particle size on hydrophobic organic compound sorption kinetics: Applicability of using representative size.

PubMed

Kang, Seju; Jung, Jihyeun; Choe, Jong Kwon; Ok, Yong Sik; Choi, Yongju

2018-04-01

Particle size of biochar may strongly affect the kinetics of hydrophobic organic compound (HOC) sorption. However, challenges exist in characterizing the effect of biochar particle size on the sorption kinetics because of the wide size range of biochar. The present study suggests a novel method to determine a representative value that can be used to show the dependence of HOC sorption kinetics to biochar particle size on the basis of an intra-particle diffusion model. Biochars derived from three different feedstocks are ground and sieved to obtain three daughter products each having different size distributions. Phenanthrene sorption kinetics to the biochars are well described by the intra-particle diffusion model with significantly greater sorption rates observed for finer grained biochars. The time to reach 95% of equilibrium for phenanthrene sorption to biochar is reduced from 4.6-17.9days for the original biochars to <1-4.6days for the powdered biochars with <125μm in size. A moderate linear correlation is found between the inverse square of the representative biochar particle radius obtained using particle size distribution analysis and the apparent phenanthrene sorption rates determined by the sorption kinetics experiments and normalized to account for the variation of the sorption rate-determining factors other than the biochar particle radius. The results suggest that the representative biochar particle radius reasonably describes the dependence of HOC sorption rates on biochar particle size. Copyright © 2017 Elsevier B.V. All rights reserved.

Insights into the equilibrium, kinetic and thermodynamics of nickel removal by environmental friendly Lansium domesticum peel biosorbent.

PubMed

Lam, Yun Fung; Lee, Lai Yee; Chua, Song Jun; Lim, Siew Shee; Gan, Suyin

2016-05-01

Lansium domesticum peel (LDP), a waste material generated from the fruit consumption, was evaluated as a biosorbent for nickel removal from aqueous media. The effects of dosage, contact time, initial pH, initial concentration and temperature on the biosorption process were investigated in batch experiments. Equilibrium data were fitted by the Langmuir, Freundlich, Temkin and Dubinin-Radushkevich models using nonlinear regression method with the best-fit model evaluated based on coefficient of determination (R(2)) and Chi-square (χ(2)). The best-fit isotherm was found to be the Langmuir model exhibiting R(2) very close to unity (0.997-0.999), smallest χ(2) (0.0138-0.0562) and largest biosorption capacity (10.1mg/g) at 30°C. Kinetic studies showed that the initial nickel removal was rapid with the equilibrium state established within 30min. Pseudo-second-order model was the best-fit kinetic model indicating the chemisorption nature of the biosorption process. Further data analysis by the intraparticle diffusion model revealed the involvement of several rate-controlling steps such as boundary layer and intraparticle diffusion. Thermodynamically, the process was exothermic, spontaneous and feasible. Regeneration studies indicated that LDP biosorbent could be regenerated using hydrochloric acid solution with up to 85% efficiency. The present investigation proved that LDP having no economic value can be used as an alternative eco-friendly biosorbent for remediation of nickel contaminated water. Copyright © 2016 Elsevier Inc. All rights reserved.

The influence of zeolites fly ash bead/TiO2 composite material surface morphologies on their adsorption and photocatalytic performance

NASA Astrophysics Data System (ADS)

Yang, Lu; Wang, Fazhou; Hakki, Amer; Macphee, Donald E.; Liu, Peng; Hu, Shuguang

2017-01-01

A low cost zeolite fly ash bead/TiO2 (ZFABT) composite materials with various surface structure features were prepared for describing those structures importance on TiO2 coating, adsorbability and photocatalytic performances. The results indicated that fly ash bead (FAB) surface was significantly altered by the precipitation/growth of secondary zeolite phases after alkali activation, which generates abundant open pores and stacked petal-liked spherical beads (∼2 μm, Sodalite zeolites). More importantly, this porosity increases as activation time was increased from 2 h to 12 h, through the precipitation of sodalite and then Na-P1 (lamellar crystals) and Na-X (octahedral crystals) zeolite structures. Compared to those of unsupported TiO2 or inactivated support/TiO2 samples, all of ZFABT samples exhibited a higher adsorption capacity and photocatalytic efficiency for RhB removal. However, adsorption is not only one factor to influence TiO2 surface reaction, the intraparticle diffusion rate of rhodamine B (RhB) molecules, and light penetration are also important parameters. Alkali activated 4 h ZFABT sample exhibited the highest photocatalytic activity, indicating its pore structure provided a better balance for those parameters to achieve a synergistic adsorption/photocatalytic process. The kinetics model suggested its high intraparticle diffusion rate allowed for more RhB molecules to easily reach the reaction surface, which is more important for high efficiency photocatalysis.

Biosorption of diazinon by a pre-treated alimentary industrial waste: equilibrium and kinetic modeling

NASA Astrophysics Data System (ADS)

Yeddou Mezenner, N.; Lagha, H.; Kais, H.; Trari, M.

2017-11-01

This study explores the feasibility of pre-treated coffee waste (PCW) as biosorbent for the removal of diazinon. The effect of the pesticide concentration (6-20 mg L-1), contact time, adsorbent dose (0.2-1.2 g L-1), solution pH (3-11.5), temperature (15-40 °C) and co-existing inorganic ions (H2PO4 -, NO3 -) on the diazinon biosorption over PCW is investigated. The experimental results indicate an optimal pH of 7.3 for the diazinon elimination on PCW (1 g L-1). The Langmuir model describes well the isotherm data with a high regression coefficient ( R 2 > 0.990) and a maximum monolayer biosorption capacity of 18.52 mg g-1 at 15 °C. It is also observed that the intra-particle diffusion is not the rate-controlling step. A comparison is evaluated between the pseudo-second-order and intra-particle diffusion kinetic models; the experimental data are well fitted by the pseudo-second-order kinetic model. The biosorption capacity decreases with increasing temperature for a diazinon concentration of 10 mg L-1. The negative enthalpy Δ H° (-63.57 kJ/mol) indicates that the diazinon biosorption onto PCW is exothermic. Under optimal conditions, the biosorption reaches 95% after 90 min. The removal efficiency decreases from 95 to 65.67 and 48.9% for the diazinon alone and in the presence of NO3 - and H2PO4 - (100 mg L-1), respectively.

Optimization of post-column reactor radius in capillary high performance liquid chromatography Effect of chromatographic column diameter and particle diameter

PubMed Central

Xu, Hongjuan; Weber, Stephen G.

2006-01-01

A post-column reactor consisting of a simple open tube (Capillary Taylor Reactor) affects the performance of a capillary LC in two ways: stealing pressure from the column and adding band spreading. The former is a problem for very small radius reactors, while the latter shows itself for large reactor diameters. We derived an equation that defines the observed number of theoretical plates (Nobs) taking into account the two effects stated above. Making some assumptions and asserting certain conditions led to a final equation with a limited number of variables, namely chromatographic column radius, reactor radius and chromatographic particle diameter. The assumptions and conditions are that the van Deemter equation applies, the mass transfer limitation is for intraparticle diffusion in spherical particles, the velocity is at the optimum, the analyte’s retention factor, k′, is zero, the post-column reactor is only long enough to allow complete mixing of reagents and analytes and the maximum operating pressure of the pumping system is used. Optimal ranges of the reactor radius (ar) are obtained by comparing the number of observed theoretical plates (and theoretical plates per time) with and without a reactor. Results show that the acceptable reactor radii depend on column diameter, particle diameter, and maximum available pressure. Optimal ranges of ar become narrower as column diameter increases, particle diameter decreases or the maximum pressure is decreased. When the available pressure is 4000 psi, a Capillary Taylor Reactor with 12 μm radius is suitable for all columns smaller than 150 μm (radius) packed with 2–5 μm particles. For 1 μm packing particles, only columns smaller than 42.5 μm (radius) can be used and the reactor radius needs to be 5 μm. PMID:16494886

Adsorption of lignite-derived humic acids on coal-based mesoporous activated carbons.

PubMed

Lorenc-Grabowska, Ewa; Gryglewicz, Grazyna

2005-04-15

The adsorption by a coal-based mesoporous activated carbon of humic acids (HAs) isolated from two Polish lignites was studied. For comparison, a commercial Aldrich humic acid was also included into this study. The differences in chemical structure and functional groups of HAs were determined by elemental analysis and infrared spectroscopy DRIFT. Two activated carbons used differed in terms of mesopore volume, mesopore size distribution, and chemical properties of the surface. The kinetics of adsorption of HAs have been discussed using three kinetic models, i.e., the first-order Lagergren model, the pseudo-second-order model, and the intraparticle diffusion model. It was found that the adsorption of HAs from alkaline solution on mesoporous activated carbon proceeds according to the pseudo-second-order model. The correlation coefficients were close to 1. The intraparticle diffusion of HA molecules within the carbon particle was identified to be the rate-limiting step. Comparing the two activated carbons, the carbon with a higher volume of pores with widths of 10-50 nm showed a greater removal efficiency of HA. An increase in the Freundlich adsorption capacity with decreasing carbon content of HA was observed. Among the HAs studied, S-HA shows characteristics indicating the highest contribution of small-size fraction. The S-HA was removed by both activated carbons to the highest extent. The effect of pH solution on the adsorption of HA was examined over the range pH 5.4-12.2. It was found that the extent of adsorption decreased with decreasing pH of the solution.

Enhanced adsorptive removal of methyl orange and methylene blue from aqueous solution by alkali-activated multiwalled carbon nanotubes.

PubMed

Ma, Jie; Yu, Fei; Zhou, Lu; Jin, Lu; Yang, Mingxuan; Luan, Jingshuai; Tang, Yuhang; Fan, Haibo; Yuan, Zhiwen; Chen, Junhong

2012-11-01

An alkali-acitvated method was explored to synthesize activated carbon nanotubes (CNTs-A) with a high specific surface area (SSA), and a large number of mesopores. The resulting CNTs-A were used as an adsorbent material for removal of anionic and cationic dyes in aqueous solutions. Experimental results indicated that CNTs-A have excellent adsorption capacity for methyl orange (149 mg/g) and methylene blue (399 mg/g). Alkali-activation treatment of CNTs increased the SSA and pore volume (PV), and introduced oxygen-containing functional groups on the surface of CNTs-A, which would be beneficial to improving the adsorption affinity of CNTs-A for removal of dyes. Kinetic regression results shown that the adsorption kinetic was more accurately represented by a pseudo second-order model. The overall adsorption process was jointly controlled by external mass transfer and intra-particle diffusion, and intra-particle diffusion played a dominant role. Freundlich isotherm model showed a better fit with adsorption data than Langmuir isotherm model. Adsorption interactions of dyes onto CNTs-A from aqueous solutions were investigated using Fourier transform infrared (FT-IR) spectroscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD), and Brunauer-Emmett-Teller (BET) method. The remarkable adsorption capacity of dye onto CNTs-A can be attributed to the multiple adsorption interaction mechanisms (hydrogen bonding, π-π electron-donor-acceptor interactions, electrostatic interactions, mesopore filling) on the CNTs-A. Results of this work are of great significance for environmental applications of activated CNTs as a promising adsorbent nanomaterial for organic pollutants from aqueous solutions.

Effect of temperature on iron leaching from bauxite residue by sulfuric acid.

PubMed

Liu, Zhi-Rong; Zeng, Kai; Zhao, Wei; Li, Ying

2009-01-01

Bauxite residue, as solid waste from alumina production, contains mainly hematite [Fe2O3]. Kinetic study of iron leaching of bauxite residue by diluted sulfuric acid at atmospheric pressure has been investigated. The results have been obtained as following: (i) Temperature play an important role in iron leaching from bauxite residue. Higher temperature is favor of Fe(III) leaching from bauxite residue. (ii) The leaching process is applicable to the intra-particle diffusion model and the apparent activation energy of model of leaching is found to be 17.32 kJ/mol.

Dye adsorption mechanisms in TiO2 films, and their effects on the photodynamic and photovoltaic properties in dye-sensitized solar cells.

PubMed

Hwang, Kyung-Jun; Shim, Wang-Geun; Kim, Youngjin; Kim, Gunwoo; Choi, Chulmin; Kang, Sang Ook; Cho, Dae Won

2015-09-14

The adsorption mechanism for the N719 dye on a TiO2 electrode was examined by the kinetic and diffusion models (pseudo-first order, pseudo-second order, and intra-particle diffusion models). Among these methods, the observed adsorption kinetics are well-described using the pseudo-second order model. Moreover, the film diffusion process was the main controlling step of adsorption, which was analysed using a diffusion-based model. The photodynamic properties in dye-sensitized solar cells (DSSCs) were investigated using time-resolved transient absorption techniques. The photodynamics of the oxidized N719 species were shown to be dependent on the adsorption time, and also the adsorbed concentration of N719. The photovoltaic parameters (Jsc, Voc, FF and η) of this DSSC were determined in terms of the dye adsorption amounts. The solar cell performance correlates significantly with charge recombination and dye regeneration dynamics, which are also affected by the dye adsorption amounts. Therefore, the photovoltaic performance of this DSSC can be interpreted in terms of the adsorption kinetics and the photodynamics of oxidized N719.

The rationale for the optimum efficiency of columns packed with new 1.9μm fully porous Titan-C18 particles-a detailed investigation of the intra-particle diffusivity.

PubMed

Gritti, Fabrice; Guiochon, Georges

2014-08-15

In a previous report, it was reported that columns packed with fully porous 1.9μm Titan-C18 particles provided a minimum reduced plate height as small as 1.7 for the most retained compound (n-octanophenone) under RPLC conditions. These particles are characterized by a relatively narrow size distribution with a relative standard deviation (RSD) of only 10%. A column packed with classical 5μm Symmetry-C18 particles, used as a reference RPLC column, generated a minimum reduced plate height of 2.1 for the same retained compound. This work demonstrates that this was due to an unusually low intra-particle diffusivity across these particles, which leads to a small longitudinal diffusion coefficient along the column. The demonstration is based on the combination of accurate measurements of the height equivalent to a theoretical plate (HETP), inverse size exclusion chromatography (ISEC), peak parking (PP), and minor disturbance method (MDM) experiments. The experimental results show that the reduced eddy dispersion HETP term (A=0.8 for a reduced velocity of 5), the internal particle porosity (ϵp=0.35), and the enrichment of acetonitrile in the pore volume (75% acetonitrile in the bulk, 85% inside the mesoporous volume) are identical on both the Titan-C18 and Symmetry-C18 columns. The difference between the internal structures of these two brands of RPLC-C18 fully porous particles lies in the values of the internal obstruction factor γp, which is 0.42 for the Symmetry-C18 but only 0.26 for the Titan-C18 particles. This is in part related to the diffusion hindrance due to the small average pore size of the Titan-C18 particles, around 59Å versus 77Å for Symmetry-C18 particles. A simple model of constriction along diffusion paths having the shape of a truncated cone suggests that the width of the pore size distribution (RSD of 30% and 20% for Titan-C18 and Symmetry-C18 particles) is mostly responsible for the difference in their obstruction factors. Copyright © 2014 Elsevier B.V. All rights reserved.

Adsorption and desorption properties of macroporous resins for anthocyanins from the calyx extract of roselle (Hibiscus sabdariffa L.).

PubMed

Chang, Xiu-Lian; Wang, Dong; Chen, Bi-Yun; Feng, Yong-Mei; Wen, Shao-Hong; Zhan, Peng-Yuan

2012-03-07

Adsorption of roselle anthocynins, a natural pigment, onto various macroporous resins was optimized to develop a simple and efficient process for industrial separation and purification of roselle anthocyanins. Nine different macroporous resins (AB-8, X-5, HPD-100, SP-207, XAD-4, LS-305A, DM-21, LS-610B, and LS-305) were evaluated for the adsorption properties of the anthocyanins extracted from the calyx extract of Hibiscus sabdariffa L. The influences of phase contact time, solution pH, initial anthocyanin concentration, and ethanol concentration with different citric acid amounts were studied by the static adsorption/desorption method. The adsorption isotherm data were fitted well to the Langmuir isotherm, and according to this model, LS-610B and LS-305 exhibited the highest monolayer sorption capacities of 31.95 and 38.16 mg/g, respectively. The kinetic data were modeled using pseudo-first-order, pseudo-second-order, and intraparticle diffusion equations. The experimental data were well described by the pseudo-second-order kinetic model. Continuous column adsorption-regeneration cycles indicated negligible capacity loss of LS-305 during operation. The overall yield of pigment product was 49.6 mg/g dried calyces. The content of roselle anthocynins in the pigment product was 4.85%.

Removal of trivalent chromium from water using low-cost natural diatomite.

PubMed

Gürü, Metin; Venedik, Duygu; Murathan, Ayşe

2008-12-30

Trivalent chromium was removed from the artificial wastewater using low-cost diatomite in batch and continuous systems. In batch system, four different sizes and five different amount of sorbent were used. The effect of the temperature on sorption was evaluated with using three different temperatures. As a result of the experiments, 85% of the trivalent chromium was removed from the wastewater in conditions of using 1.29mm grain material at 30 degrees C temperature for 60min in batch system but chromium removal was 82% at 30 degrees C temperature for 22min and 97% from the wastewater at 30 degrees C temperature for 80min in continuous system. Also, the equilibrium adsorption isotherms have been analyzed by Langmuir and Freundlich models. The Langmuir isotherms have the highest correlation coefficients. Langmuir adsorption isotherm constants corresponding to adsorption capacity, q0, were found to be 28.1, 26.5 and 21.8mg Cr3+/g diatomite at 15, 30 and 45 degrees C, respectively. Adsorption process was an exothermic process as a result of thermodynamic parameters calculations. The kinetic data of the sorption showed that the pseudo second-order equation was the more appropriate, which indicate that the intraparticle diffusion is the rate-limiting factor.

Ultrasonic-assisted synthesis of novel nanocomposite of poly(vinyl alcohol) and amino-modified MCM-41: A green adsorbent for Cd(II) removal.

PubMed

Soltani, Roozbeh; Dinari, Mohammad; Mohammadnezhad, Gholamhossein

2018-01-01

Amino-modified MCM-41/poly(vinyl alcohol) nanocomposite (M-MCM-41/PVOH NC) was developed for the adsorption of Cd(II) from aqueous media. M-MCM-41/PVOH NC was prepared through ultrasonic-assisted and simple blending procedure with economical and environmentally friendly polymer. The as-prepared adsorbent was characterized by FT-IR, TEM, FE-SEM and TGA. The contact time, solution pH and initial concentration of Cd(II) were found to affect the adsorption of Cd(II) from aqueous media. Kinetic studies were carried out and pseudo-first-order (PFO), pseudo-second-order (PSO), Elovich, and intra-particle diffusion (IPD) reaction kinetic models were examined. The kinetic results revealed that the adsorption of Cd(II) onto M-MCM-41/PVOH NC followed PSO kinetic model and is a chemical adsorption. The equilibrium adsorption data were evaluated by different isotherms viz. Langmuir, Freundlich, and Dubinin Radushkevich (D-R) equations. The equilibrium data fitted better with the Langmuir isotherm and the maximum adsorption capacity of M-MCM-41/PVOH NC at 298K was calculated to be 46.73mgg -1 for Cd(II) on a typical saturated monomolecular layer with a fixed number of localized adsorption sites. Copyright © 2017 Elsevier B.V. All rights reserved.

Activated carbon prepared from yerba mate used as a novel adsorbent for removal of tannery dye from aqueous solution.

PubMed

Linhares, Bruno; Weber, Caroline Trevisan; Foletto, Edson Luiz; Paz, Diego Silva; Mazutti, Marcio A; Collazzo, Gabriela Carvalho

2013-01-01

Activated carbon prepared from yerba mate (Ilex paraguariensis) was used as adsorbent for the removal of tannery dye from aqueous solution. The activated carbon was characterized, and it showed a mesoporous texture, with surface area of 537.4 m2 g(-1). The initial dye concentration, contact time and pH influenced the adsorption capacity. The equilibrium data were in good agreement with both Langmuir and Freundlich isotherms. The adsorption kinetics of the tannery dye on activated carbon prepared from yerba mate followed a pseudo-second-order model. The adsorption process was found to be controlled by both external mass-transfer and intraparticle diffusion, but the external diffusion was the dominating process. This work highlights the potential application of activated carbon produced from yerba mate in the field of adsorption.

The role of external and internal mass transfer in the process of Cu2+ removal by natural mineral sorbents.

PubMed

Sljivić, M; Smiciklas, I; Plećas, I; Pejanović, S

2011-07-01

The kinetics of Cu2+ sorption on to zeolite, clay and diatomite was investigated as a function of initial metal concentrations. For consideration of the mass transfer phenomena, single resistance models based on both film and intraparticle diffusion were tested and compared. The obtained results suggested that the rate-limiting step in Cu2+ sorption strongly depended on the sorbent type, as well as on initial cation concentration. The decrease in external mass transfer coefficients with the increase in initial metal concentrations was in excellent agreement with expressions based on Sherwood and Schmidt dimensionless numbers. The internal diffusivities through zeolite particles were in the range 1.0 x 10(-11) to 1.0 x 10(-13) m2/min, depending on the Cu2+ concentration and the applied theoretical model.

Consequence of chitosan treating on the adsorption of humic acid by granular activated carbon.

PubMed

Maghsoodloo, Sh; Noroozi, B; Haghi, A K; Sorial, G A

2011-07-15

In this work, equilibrium and kinetic adsorption of humic acid (HA) onto chitosan treated granular activated carbon (MGAC) has been investigated and compared to the granular activated carbon (GAC). The adsorption equilibrium data showed that adsorption behaviour of HA could be described reasonably well by Langmuir adsorption isotherm for GAC and Freundlich adsorption isotherm for MGAC. It was shown that pre-adsorption of chitosan onto the surface of GAC improved the adsorption capacity of HA changing the predominant adsorption mechanism. Monolayer capacities for the adsorption of HA onto GAC and MGAC were calculated 55.8 mg/g and 71.4 mg/g, respectively. Kinetic studies showed that film diffusion and intra-particle diffusion were simultaneously operating during the adsorption process for MGAC. Copyright © 2011 Elsevier B.V. All rights reserved.

Characterization of metal adsorption kinetic properties in batch and fixed-bed reactors.

PubMed

Chen, J Paul; Wang, Lin

2004-01-01

Copper adsorption kinetic properties in batch and fixed-bed reactors were studied in this paper. The isothermal adsorption experiments showed that the copper adsorption capacity of a granular activated carbon (Filtrasorb 200) increased when ionic strength was higher. The presence of EDTA diminished the adsorption. An intraparticle diffusion model and a fixed-bed model were successfully used to describe the batch kinetic and fixed-bed operation behaviors. The kinetics became faster when the solution pH was not controlled, implying that the surface precipitation caused some metal uptake. The external mass transfer coefficient, the diffusivity and the dispersion coefficient were obtained from the modeling. It was found that both external mass transfer and dispersion coefficients increased when the flow rate was higher. Finally effects of kinetic parameters on simulation of fixed-bed operation were conducted.

Sorption isotherms, kinetic and optimization process of amino acid proline based polymer nanocomposite for the removal of selected textile dyes from industrial wastewater.

PubMed

Raghunath, Sharista; Anand, K; Gengan, R M; Nayunigari, Mithil Kumar; Maity, Arjun

2016-12-01

In this article, adsorption and kinetic studies were carried out on three textile dyes, namely Reactive Blue 222 (RB 222), Reactive Red 195 (RR 195) and Reactive Yellow 145 (RY 145). The dyes studied in a mixture were adsorbed under various conditions onto PRO-BEN, a bentonite modified with a new cationic proline polymer (l-proline-epichlorohydrin polymer). The proline polymer was characterized by 1 H NMR, Fourier transform infrared spectroscopy (FT-IR), dynamic light scattering (DLS) and TEM. The PRO-BEN composite was characterized by FT-IR, dynamic light scattering (DLS) (zeta potential), TEM imaging, SEM/EDX and X-ray photoelectron spectroscopy (characterize the binding energy). During adsorption studies, factors involving pH, temperature, the initial concentrations of the dyes and the quantity of PRO-BEN used during adsorption were established. The results revealed that the adsorption mechanism was categorized by the Langmuir type 1 isotherm. The adsorption data followed the pseudo-second order kinetic model. The intraparticle diffusion model indicated that adsorption did not only depend on the intraparticle diffusion of the dyes. The thermodynamic parameters verified that the adsorption process was spontaneous and exothermic. The Gibbs free energy values indicated that physisorption had occurred. Successful adsorption of dyes from an industrial effluent was achieved. Desorption studies concluded that PRO-BEN desorbed the dyes better than alumina. This can thereby be viewed as a recyclable remediation material. The PRO-BEN composite could be a cost efficient alternative towards the removal of organic dyes in wastewater treatment. Copyright © 2016 Elsevier B.V. All rights reserved.

Adsorption kinetics of malachite green onto activated carbon prepared from Tunçbilek lignite.

PubMed

Onal, Y; Akmil-Başar, C; Eren, Didem; Sarici-Ozdemir, Cigdem; Depci, Tolga

2006-02-06

Adsorbent (T3K618) has been prepared from Tunçbilek lignite by chemical activation with KOH. Pore properties of the activated carbon such as BET surface area, pore volume, pore size distribution, and pore diameter were characterized by t-plot based on N2 adsorption isotherm. The N2 adsorption isotherm of malachite green on T3K618 is type I. The BET surface area of the adsorbent which was primarily contributed by micropores was determined 1000 m2/g. T3K618 was used to adsorb malachite green (MG) from an aqueous solution in a batch reactor. The effects of initial dye concentration, agitation time, initial pH and adsorption temperature have been studied. It was also found that the adsorption isotherm followed both Freundlich and Dubinin-Radushkevich models. However, the Freundlich gave a better fit to all adsorption isotherms than the Dubinin-Radushkevich. The kinetics of adsorption of MG has been tested using pseudo-first-order, pseudo-second-order and intraparticle diffusion models. Results show that the adsorption of MG from aqueous solution onto micropores T3K618 proceeds according to the pseudo-second-order model. The intraparticle diffusion of MG molecules within the carbon particles was identified to be the rate-limiting step. The adsorption of the MG was endothermic (DeltaH degrees = 6.55-62.37 kJ/mol) and was accompanied by an increase in entropy (DeltaS degrees = 74-223 J/mol K) and a decrease in mean value of Gibbs energy (DeltaG degrees = -6.48 to -10.32 kJ/mol) in the temperature range of 20-50 degrees C.

Fractional Diffusion Equations and Anomalous Diffusion

NASA Astrophysics Data System (ADS)

Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

2018-01-01

Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ho, C.-L.; Lee, C.-C., E-mail: chieh.no27@gmail.com

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

Application of ZnO nanorods loaded on activated carbon for ultrasonic assisted dyes removal: Experimental design and derivative spectrophotometry method.

PubMed

Ansari, Fatemeh; Ghaedi, Mehrorang; Taghdiri, Mehdi; Asfaram, Arash

2016-11-01

A method based on application of ZnO nanorods loaded on activated carbon (ZnO-NRs-AC) for adsorption of Bromocresol Green (BCG) and Eosin Y (EY) accelerated by ultrasound was described. The present material was synthesized under ultrasound assisted wet-chemical method and subsequently was characterized by FE-SEM, TEM, BET and XRD analysis. The extent of contribution of conventional variables like pH (2.0-10.0), BCG concentration (4-20mgL(-1)), EY concentration (3-23mgL(-1)), adsorbent dosage (0.01-0.03g), sonication time (1-5min) and centrifuge time (2-6min) as main and interaction part were investigated by central composite design under response surface methodology. Analysis of variance (ANOVA) was adapted to experimental data and guide the best operational conditions mass by set at 6.0, 9mgL(-1), 10mgL(-1), 0.02g, 4 and 4min for pH, BCG concentration, EY concentration, adsorbent dosage, sonication and centrifuge time, respectively. At these specified conditions dye adsorption efficiency was higher than 99.5%. The suitability and well prediction of optimum point was tested by conducting five experiments and respective results revel that RSD% was lower than 3% and high quality of fitting was confirmed by t-test. The experimental data were best fitted in Langmuir isotherm equation and the removal followed pseudo second order kinetics. The experimentally obtained maximum adsorption capacities were estimated as 57.80 and 61.73mgg(-1) of ZnO-NRs-AC for BCG and EY respectively from binary dye solutions. The mechanism of removal was explained by boundary layer diffusion via intraparticle diffusion. Copyright © 2016 Elsevier B.V. All rights reserved.

Effects of polymer graft properties on protein adsorption and transport in ion exchange chromatography: a multiscale modeling study.

PubMed

Basconi, Joseph E; Carta, Giorgio; Shirts, Michael R

2015-04-14

Multiscale simulation is used to study the adsorption of lysozyme onto ion exchangers obtained by grafting charged polymers into a porous matrix, in systems with various polymer properties and strengths of electrostatic interaction. Molecular dynamics simulations show that protein partitioning into the polymer-filled pore space increases with the overall charge content of the polymers, while the diffusivity in the pore space decreases. However, the combination of greatly increased partitioning and modestly decreased diffusion results in macroscopic transport rates that increase as a function of charge content, as the large concentration driving force due to enhanced pore space partitioning outweighs the reduction in the pore space diffusivity. Matrices having greater charge associated with the grafted polymers also exhibit more diffuse intraparticle concentration profiles during transient adsorption. In systems with a high charge content per polymer and a low protein loading, the polymers preferentially partition toward the surface due to favorable interactions with the surface-bound protein. These results demonstrate the potential of multiscale modeling to illuminate qualitative trends between molecular properties and the adsorption equilibria and kinetic properties observable on macroscopic scales.

Adsorption isotherms and kinetics of activated carbons produced from coals of different ranks.

PubMed

Purevsuren, B; Lin, Chin-Jung; Davaajav, Y; Ariunaa, A; Batbileg, S; Avid, B; Jargalmaa, S; Huang, Yu; Liou, Sofia Ya-Hsuan

2015-01-01

Activated carbons (ACs) from six coals, ranging from low-rank lignite brown coal to high-rank stone coal, were utilized as adsorbents to remove basic methylene blue (MB) from an aqueous solution. The surface properties of the obtained ACs were characterized via thermal analysis, N2 isothermal sorption, scanning electron microscopy, Fourier transform infrared spectroscopy, X-ray photoelectron spectroscopy and Boehm titration. As coal rank decreased, an increase in the heterogeneity of the pore structures and abundance of oxygen-containing functional groups increased MB coverage on its surface. The equilibrium data fitted well with the Langmuir model, and adsorption capacity of MB ranged from 51.8 to 344.8 mg g⁻¹. Good correlation coefficients were obtained using the intra-particle diffusion model, indicating that the adsorption of MB onto ACs is diffusion controlled. The values of the effective diffusion coefficient ranged from 0.61 × 10⁻¹⁰ to 7.1 × 10⁻¹⁰ m² s⁻¹, indicating that ACs from lower-rank coals have higher effective diffusivities. Among all the ACs obtained from selected coals, the AC from low-rank lignite brown coal was the most effective in removing MB from an aqueous solution.

Adsorption-desorption mechanism of phosphate by immobilized nano-sized magnetite layer: interface and bulk interactions.

PubMed

Zach-Maor, Adva; Semiat, Raphael; Shemer, Hilla

2011-11-15

Phosphate adsorption mechanism by a homogenous porous layer of nano-sized magnetite particles immobilized onto granular activated carbon (nFe-GAC) was studied for both interface and bulk structures. X-ray Photoelectron Spectroscopy (XPS) analysis revealed phosphate bonding to the nFe-GAC predominantly through bidentate surface complexes. It was established that phosphate was adsorbed to the magnetite surface mainly via ligand exchange mechanism. Initially, phosphate was adsorbed by the active sites on the magnetite surface, after which it diffused into the interior of the nano-magnetite layer, as indicated by intraparticle diffusion model. This diffusion process continues regardless of interface interactions, revealing some of the outer magnetite binding sites for further phosphate uptake. Desorption, using NaOH solution, was found to be predominantly a surface reaction, at which hydroxyl ions replace the adsorbed phosphate ions only at the surface outer biding sites. Five successive fix-bed adsorption/regeneration cycles were successfully applied, without significant reduction in the nFe-GAC adsorption capacity and at high regeneration efficiency. Copyright © 2011 Elsevier Inc. All rights reserved.

Comparison of ultrasonic with stirrer performance for removal of sunset yellow (SY) by activated carbon prepared from wood of orange tree: artificial neural network modeling.

PubMed

Ghaedi, A M; Ghaedi, M; Karami, P

2015-03-05

The present work focused on the removal of sunset yellow (SY) dye from aqueous solution by ultrasound-assisted adsorption and stirrer by activated carbon prepared from wood of an orange tree. Also, the artificial neural network (ANN) model was used for predicting removal (%) of SY dye based on experimental data. In this study a green approach was described for the synthesis of activated carbon prepared from wood of an orange tree and usability of it for the removal of sunset yellow. This material was characterized using scanning electron microscopy (SEM) and transmission electron microscopy (TEM). The impact of variables, including initial dye concentration (mg/L), pH, adsorbent dosage (g), sonication time (min) and temperature (°C) on SY removal were studied. Fitting the experimental equilibrium data of different isotherm models such as Langmuir, Freundlich, Temkin and Dubinin-Radushkevich models display the suitability and applicability of the Langmuir model. Analysis of experimental adsorption data by different kinetic models including pseudo-first and second order, Elovich and intraparticle diffusion models indicate the applicability of the second-order equation model. The adsorbent (0.5g) is applicable for successful removal of SY (>98%) in short time (10min) under ultrasound condition. Copyright © 2014 Elsevier B.V. All rights reserved.

MCM-41 impregnated with A zeolite precursor: Synthesis, characterization and tetracycline antibiotics removal from aqueous solution

PubMed Central

Liu, Minmin; Hou, Li-an; Yu, Shuili; Xi, Beidou; Zhao, Ying; Xia, Xunfeng

2013-01-01

In this paper, the MCM-41 has been modified by impregnation with zeolite A to prepare a kind of new adsorbent. The adsorption of TC from aqueous solutions onto modified MCM-41 has been studied. It was discovered that the adsorption capability of zeolite A modified MCM-41 (A-MCM-41) increased dramatically after modification. The modified MCM-41 was characterized by X-ray diffraction (XRD), nitrogen adsorption–desorption, Fourier Transform Infrared (FTIR) analysis, Transmission electron microscopy (TEM) images, and 29Si and 27Al Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) spectra. The modified MCM-41 structure was still retained after impregnated with zeolite A but the surface area and pore diameter decreased due to pore blockage. The adsorption of TC on modified MCM-41 was discussed regarding various parameters such as pH, initial TC concentration, and the reaction time. The pH effects on TC adsorption indicated that the adsorbents had better adsorption performances in acidic and neutral conditions. The adsorption isotherms were fitted well by the Langmuir model. The adsorption kinetics was well described by both pseudo-second order equation and the intra-particle diffusion model. The adsorption behavior in a fixed-bed column system followed Thomas model. The adsorption behavior of TC was the chemical adsorption with an ion exchange process and electrostatic adsorption. PMID:24976787

Preparation of activated carbon from a renewable bio-plant of Euphorbia rigida by H 2SO 4 activation and its adsorption behavior in aqueous solutions

NASA Astrophysics Data System (ADS)

Gerçel, Özgül; Özcan, Adnan; Özcan, A. Safa; Gerçel, H. Ferdi

2007-03-01

The use of activated carbon obtained from Euphorbia rigida for the removal of a basic textile dye, which is methylene blue, from aqueous solutions at various contact times, pHs and temperatures was investigated. The plant material was chemically modified with H 2SO 4. The surface area of chemically modified activated carbon was 741.2 m 2 g -1. The surface characterization of both plant- and activated carbon was undertaken using FTIR spectroscopic technique. The adsorption process attains equilibrium within 60 min. The experimental data indicated that the adsorption isotherms are well described by the Langmuir equilibrium isotherm equation and the calculated adsorption capacity of activated carbon was 114.45 mg g -1 at 40° C. The adsorption kinetics of methylene blue obeys the pseudo-second-order kinetic model and also followed by the intraparticle diffusion model up to 60 min. The thermodynamic parameters such as Δ G°, Δ H° and Δ S° were calculated to estimate the nature of adsorption. The activation energy of the system was calculated as 55.51 kJ mol -1. According to these results, prepared activated carbon could be used as a low-cost adsorbent to compare with the commercial activated carbon for the removal textile dyes from textile wastewater processes.

Study of 2,4-dichlorophenoxyacetic acid (2,4-D) removal by Cu-Fe-layered double hydroxide from aqueous solution

NASA Astrophysics Data System (ADS)

Nejati, Kamellia; Davary, Soheila; Saati, Marziye

2013-09-01

The hydrotalcite-like compound of Cu-Fe-layered double hydroxide was studied as a potential adsorbent of herbicide 2,4-dichlorophenoxyacetic acid (2,4-D). The nanoparticles of Cu-Fe layered double hydroxide were prepared by Cu/Fe molar ratio of 2:1 using a coprecipitation method at pH 8.5 and characterized by the X-ray powder diffraction (XRD), the Fourier transform infrared spectroscopy (FT-IR), the thermal gravimetric analysis (TGA) and the elemental analysis. The size and morphology of nanoparticles were examined by the transmission electron microscopy (TEM). The adsorption experiments on LDH, on the other hand, were conducted in three different procedures, namely, time-dependent, pH-dependent and temperature-dependent. Characterization of the adsorption products by the XRD method indicates that the intercalation of 2,4-D between the LDH layers has not occurred and the surface adsorption had taken place. The adsorption kinetic was tested for pseudo-first-order, pseudo-second-order, Elovich and Intra-particle diffusion kinetic models and the rate constants were calculated. The equilibrium adsorption data were described by Langmuir and Freundlich equations. It was observed that, the Langmuir isotherm slightly better fitted to the experimental data rather than that of Freundlich. In the adsorption experiments, the Gibbs free energy values, ΔG°, the enthalpy, ΔH°, and the entropy, ΔS° were also determined.

MCM-41 impregnated with A zeolite precursor: Synthesis, characterization and tetracycline antibiotics removal from aqueous solution.

PubMed

Liu, Minmin; Hou, Li-An; Yu, Shuili; Xi, Beidou; Zhao, Ying; Xia, Xunfeng

2013-05-01

In this paper, the MCM-41 has been modified by impregnation with zeolite A to prepare a kind of new adsorbent. The adsorption of TC from aqueous solutions onto modified MCM-41 has been studied. It was discovered that the adsorption capability of zeolite A modified MCM-41 (A-MCM-41) increased dramatically after modification. The modified MCM-41 was characterized by X-ray diffraction (XRD), nitrogen adsorption-desorption, Fourier Transform Infrared (FTIR) analysis, Transmission electron microscopy (TEM) images, and 29 Si and 27 Al Magic Angle Spinning Nuclear Magnetic Resonance (MAS NMR) spectra. The modified MCM-41 structure was still retained after impregnated with zeolite A but the surface area and pore diameter decreased due to pore blockage. The adsorption of TC on modified MCM-41 was discussed regarding various parameters such as pH, initial TC concentration, and the reaction time. The pH effects on TC adsorption indicated that the adsorbents had better adsorption performances in acidic and neutral conditions. The adsorption isotherms were fitted well by the Langmuir model. The adsorption kinetics was well described by both pseudo-second order equation and the intra-particle diffusion model. The adsorption behavior in a fixed-bed column system followed Thomas model. The adsorption behavior of TC was the chemical adsorption with an ion exchange process and electrostatic adsorption.

Load-dependent surface diffusion model for analyzing the kinetics of protein adsorption onto mesoporous materials.

PubMed

Marbán, Gregorio; Ramírez-Montoya, Luis A; García, Héctor; Menéndez, J Ángel; Arenillas, Ana; Montes-Morán, Miguel A

2018-02-01

The adsorption of cytochrome c in water onto organic and carbon xerogels with narrow pore size distributions has been studied by carrying out transient and equilibrium batch adsorption experiments. It was found that equilibrium adsorption exhibits a quasi-Langmuirian behavior (a g coefficient in the Redlich-Peterson isotherms of over 0.95) involving the formation of a monolayer of cyt c with a depth of ∼4nm on the surface of all xerogels for a packing density of the protein inside the pores of 0.29gcm -3 . A load-dependent surface diffusion model (LDSDM) has been developed and numerically solved to fit the experimental kinetic adsorption curves. The results of the LDSDM show better fittings than the standard homogeneous surface diffusion model. The value of the external mass transfer coefficient obtained by numerical optimization confirms that the process is controlled by the intraparticle surface diffusion of cyt c. The surface diffusion coefficients decrease with increasing protein load down to zero for the maximum possible load. The decrease is steeper in the case of the xerogels with the smallest average pore diameter (∼15nm), the limit at which the zero-load diffusion coefficient of cyt c also begins to be negatively affected by interactions with the opposite wall of the pore. Copyright © 2017 Elsevier Inc. All rights reserved.

Particle size effects on protein and virus-like particle adsorption on perfusion chromatography media.

PubMed

Wu, Yige; Abraham, Dicky; Carta, Giorgio

2015-01-02

The resin structure, chromatographic behavior, and adsorption kinetics of proteins and virus-like-particles (VLPs) are studied for POROS HS 20 and POROS HS 50 (23 and 52 μm mean diameter, respectively) to determine the effects of particle size on perfusion chromatography and to determine the predictive ability of available models. Transmission electron microscopy (TEM) and inverse size-exclusion chromatography (iSEC) show similar structures for the two resins, both containing 200-1000 nm pores that transect a network of much smaller pores. For non-binding conditions, trends of the height equivalent to a theoretical plate (HETP) as a function of reduced velocity are consistent with perfusion. The estimated intraparticle flow fractions for these conditions are 0.0018 and 0.00063 for POROS HS 20 and HS 50, respectively. For strong binding conditions, confocal laser scanning microscopy (CLSM) shows asymmetrical intraparticle concentrations profiles and enhanced rates of IgG adsorption on POROS HS 20 at 1000 cm/h. The corresponding effective diffusivity under flow is 2-3 times larger than for non-flow conditions and much larger than observed for POROS HS 50, consistent with available models. For VLPs, however, adsorption is confined to a thin layer near the particle surface for both resins, suggesting that the bound VLPs block the pores. Copyright © 2014 Elsevier B.V. All rights reserved.

Hybrid diffusion-P3 equation in N-layered turbid media: steady-state domain.

PubMed

Shi, Zhenzhi; Zhao, Huijuan; Xu, Kexin

2011-10-01

This paper discusses light propagation in N-layered turbid media. The hybrid diffusion-P3 equation is solved for an N-layered finite or infinite turbid medium in the steady-state domain for one point source using the extrapolated boundary condition. The Fourier transform formalism is applied to derive the analytical solutions of the fluence rate in Fourier space. Two inverse Fourier transform methods are developed to calculate the fluence rate in real space. In addition, the solutions of the hybrid diffusion-P3 equation are compared to the solutions of the diffusion equation and the Monte Carlo simulation. For the case of small absorption coefficients, the solutions of the N-layered diffusion equation and hybrid diffusion-P3 equation are almost equivalent and are in agreement with the Monte Carlo simulation. For the case of large absorption coefficients, the model of the hybrid diffusion-P3 equation is more precise than that of the diffusion equation. In conclusion, the model of the hybrid diffusion-P3 equation can replace the diffusion equation for modeling light propagation in the N-layered turbid media for a wide range of absorption coefficients.

Hydrogen Reduction of Lunar Regolith Simulants for Oxygen Production

NASA Technical Reports Server (NTRS)

Hegde, U.; Balasubramaniam, R.; Gokoglu, S. A.; Rogers, K.; Reddington, M.; Oryshchyn, L.

2011-01-01

Hydrogen reduction of the lunar regolith simulants JSC-1A and LHT-2M is investigated in this paper. Experiments conducted at NASA Johnson Space Center are described and are analyzed utilizing a previously validated model developed by the authors at NASA Glenn Research Center. The effects of regolith sintering and clumping, likely in actual production operations, on the oxygen production rate are studied. Interpretations of the obtained results on the basis of the validated model are provided and linked to increase in the effective particle size and reduction in the intra-particle species diffusion rates. Initial results on the pressure dependence of the oxygen production rate are also presented and discussed

Kinetic modeling of copper biosorption by immobilized biomass

DOE Office of Scientific and Technical Information (OSTI.GOV)

Veglio, F.; Beolchini, F.; Toro, L.

1998-03-01

Biosorption of heavy metals is one of the most promising technologies involved in the removal of toxic metals from industrial waste streams and natural waters. The kinetic modeling of copper biosorption by Arthrobacter sp. immobilized in a hydroxyethyl methacrylate-based matrix is reported in this work. The resin-biomass complex (RBC) has been used for copper biosorption in different conditions according to a factorial experiment. Factors investigated were cross-linker (trimethylolpropane trimethacrylate) concentration, biomass concentration in the solid, and particles` granulometry. A maximum copper specific uptake of abut 7 mg of Cu/g of biomass (dry weight) has been observed, in the case ofmore » a RBC with the following characteristics: 2% (w/w) cross-linker concentration, 8% (w/w) biomass concentration, and 425--750 {micro}m granulometry. The shrinking core model has been used for the fitting of experimental data. A good fit has been found in the case of controlling intraparticle diffusion in all experimental trials. The copper diffusion coefficient in RBC has been estimated from the slope of the regression lines. Values obtained for the diffusion coefficients do not differ from one another with respect to the estimated standard error. An average apparent copper diffusion coefficient of about 3 {times} 10{sup {minus}6} cm{sup 2}/s has been found.« less

Adsorption properties of kaolinite-based nanocomposites for Fe and Mn pollutants from aqueous solutions and raw ground water: kinetics and equilibrium studies.

PubMed

Shaban, Mohamed; Hassouna, Mohamed E M; Nasief, Fadya M; AbuKhadra, Mostafa R

2017-10-01

Raw kaolinite was used in the synthesis of metakaolinite/carbon nanotubes (K/CNTs) and kaolinite/starch (K/starch) nanocomposites. Raw kaolinite and the synthetic composites were characterized using XRD, SEM, and TEM techniques. The synthetic composites were used as adsorbents for Fe and Mn ions from aqueous solutions and natural underground water. The adsorption by the both composites is highly pH dependent and achieves high efficiency within the neutral pH range. The experimental adsorption data for the uptake of Fe and Mn ions by K/CNTs were found to be well represented by the pseudo-second-order kinetic model rather than the intra-particle diffusion model or Elovich model. For the adsorption using K/starch, the uptake results of Fe ions was well fitted by the second-order model, whereas the uptake of Mn ions fitted well to the Elovich model rather than pseudo-second-order and intra-particle diffusion models The equilibrium studies revealed the excellent fitting of the removal of Fe and Mn ions by K/CNTs and Fe using K/starch with the Langmuir isotherm model rather than with Freundlich and Temkin models. But the adsorption of Mn ions by K/starch is well fitted with Freundlich rather than Temkin and Langmuir isotherm models. The thermodynamic studies reflected the endothermic nature and the exothermic nature for the adsorption by K/CNTs and K/starch nanocomposites, respectively. Natural ground water contaminated by 0.4 mg/L Fe and 0.5 mg/L Mn was treated at the optimum conditions of pH 6 and 120 min contact time. Under these conditions, 92.5 and 72.5% Fe removal efficiencies were achieved using 20 mg of K/CNTs and K/starch nanocomposites, respectively. Also, K/CNTs nanocomposite shows higher efficiency in the removal of Mn ions as compared to K/starch nanocomposite.

Investigating the Heavy Metal Adsorption of Mesoporous Silica Materials Prepared by Microwave Synthesis

NASA Astrophysics Data System (ADS)

Zhu, Wenjie; Wang, Jingxuan; Wu, Di; Li, Xitong; Luo, Yongming; Han, Caiyun; Ma, Wenhui; He, Sufang

2017-05-01

Mesoporous silica materials (MSMs) of the MCM-41 type were rapidly synthesized by microwave heating using silica fume as silica source and evaluated as adsorbents for the removal of Cu2+, Pb2+, and Cd2+ from aqueous solutions. The effects of microwave heating times on the pore structure of the resulting MSMs were investigated as well as the effects of different acids which were employed to adjust the solution pH during the synthesis. The obtained MCM-41 samples were characterized by nitrogen adsorption-desorption analyses, X-ray powder diffraction, and transmission electron microscopy. The results indicated that microwave heating method can significantly reduce the synthesis time of MCM-41 to 40 min. The MCM-41 prepared using citric acid (c-MCM-41(40)) possessed more ordered hexagonal mesostructure, higher pore volume, and pore diameter. We also explored the ability of c-MCM-41(40) for removing heavy metal ions (Cu2+, Pb2+, and Cd2+) from aqueous solution and evaluated the influence of pH on its adsorption capacity. In addition, the adsorption isotherms were fitted by Langmuir and Freundlich models, and the adsorption kinetics were assessed using pseudo-first-order and pseudo-second-order models. The intraparticle diffusion model was studied to understand the adsorption process and mechanism. The results confirmed that the as-synthesized adsorbent could efficiently remove the heavy metal ions from aqueous solution at pH range of 5-7. The adsorption isotherms obeyed the Langmuir model, and the maximum adsorption capacities of the adsorbent for Cu2+, Pb2+, and Cd2+ were 36.3, 58.5, and 32.3 mg/g, respectively. The kinetic data were well fitted to the pseudo-second-order model, and the results of intraparticle diffusion model showed complex chemical reaction might be involved during adsorption process.

Cellular Automata for Spatiotemporal Pattern Formation from Reaction-Diffusion Partial Differential Equations

NASA Astrophysics Data System (ADS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.

Iron Impregnated Activated Carbon as an Efficient Adsorbent for the Removal of Methylene Blue: Regeneration and Kinetics Studies

PubMed Central

Shah, Irfan; Adnan, Rohana; Wan Ngah, Wan Saime; Mohamed, Norita

2015-01-01

In this study, iron impregnated activated carbon (FeAC) was synthesized following an oxidation and iron impregnation of activated carbon (AC). Both the AC and FeAC were characterized by pHZPC and FTIR spectroscopy. The removal of Methylene Blue (MB) by AC and FeAC was examined under various experimental conditions. The FeAC showed up to 95% (higher than AC) MB removal in the pH range of 7–10. Although the reaction kinetics was pseudo–second order, the overall rate was controlled by a number of processes such as film diffusion, pore diffusion and intraparticle diffusion. The activation energy values for the MB uptake by AC and FeAC (21.79 and 14.82 kJ/mol, respectively) revealed a physisorption process. In the regeneration study, FeAC has shown consistently ≥ 90% MB removal even up to 10 repeated cycles. The reusable characteristic of the spent FeAC improved the practical use of activated carbon and can be a breakthrough for continuous flow system applications where it can work effectively without any significant reduction in its performance. PMID:25849291

ZVI (Fe0) desalination: catalytic partial desalination of saline aquifers

NASA Astrophysics Data System (ADS)

Antia, David D. J.

2018-05-01

Globally, salinization affects between 100 and 1000 billion m3 a-1 of irrigation water. The discovery that zero valent iron (ZVI, Fe0) could be used to desalinate water (using intra-particle catalysis in a diffusion environment) raises the possibility that large-scale in situ desalination of aquifers could be undertaken to support agriculture. ZVI desalination removes NaCl by an adsorption-desorption process in a multi-stage cross-coupled catalytic process. This study considers the potential application of two ZVI desalination catalyst types for in situ aquifer desalination. The feasibility of using ZVI catalysts when placed in situ within an aquifer to produce 100 m3 d-1 of partially desalinated water from a saline aquifer is considered.

Transformed Fourier and Fick equations for the control of heat and mass diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guenneau, S.; Petiteau, D.; Zerrad, M.

We review recent advances in the control of diffusion processes in thermodynamics and life sciences through geometric transforms in the Fourier and Fick equations, which govern heat and mass diffusion, respectively. We propose to further encompass transport properties in the transformed equations, whereby the temperature is governed by a three-dimensional, time-dependent, anisotropic heterogeneous convection-diffusion equation, which is a parabolic partial differential equation combining the diffusion equation and the advection equation. We perform two dimensional finite element computations for cloaks, concentrators and rotators of a complex shape in the transient regime. We precise that in contrast to invisibility cloaks for waves,more » the temperature (or mass concentration) inside a diffusion cloak crucially depends upon time, its distance from the source, and the diffusivity of the invisibility region. However, heat (or mass) diffusion outside cloaks, concentrators and rotators is unaffected by their presence, whatever their shape or position. Finally, we propose simplified designs of layered cylindrical and spherical diffusion cloaks that might foster experimental efforts in thermal and biochemical metamaterials.« less

Fractional Diffusion Processes: Probability Distributions and Continuous Time Random Walk

NASA Astrophysics Data System (ADS)

Gorenflo, R.; Mainardi, F.

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order alpha in (0,2] and skewness theta (\\verttheta\\vertlemin \\{alpha ,2-alpha \\}), and the first-order time derivative with a Caputo derivative of order beta in (0,1] . The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process. We view it as a generalized diffusion process that we call fractional diffusion process, and present an integral representation of the fundamental solution. A more general approach to anomalous diffusion is however known to be provided by the master equation for a continuous time random walk (CTRW). We show how this equation reduces to our fractional diffusion equation by a properly scaled passage to the limit of compressed waiting times and jump widths. Finally, we describe a method of simulation and display (via graphics) results of a few numerical case studies.

Application of nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, UV-Visible spectroscopy and kinetic modeling for elucidation of adsorption chemistry in uptake of tetracycline by zeolite beta.

PubMed

Kang, Jin; Liu, Huijuan; Zheng, Yu-Ming; Qu, Jiuhui; Chen, J Paul

2011-02-01

Extensive usage of tetracycline has resulted in its contamination in surface water and groundwater. The adsorption of tetracycline on zeolite beta was systematically investigated for the decontamination of the antibiotic polluted water in this study. Ninety percent of uptake by the zeolite beta occured in 0.25h, and the adsorption equilibrium was obtained within 3h, which was well described by an intraparticle diffusion model. The adsorption generally increased when pH was increased from 4.0 to 5.0, and then decreased significantly as the pH was further increased, which was caused by the pH-dependent speciation of tetracycline and surface charge of zeolite beta. Both Freundlich and Langmuir equations well described the adsorption isotherm. A thermodynamic analysis showed that the sorption process was spontaneous and endothermic. Aluminum atoms in the zeolite played a crucial role in the uptake; the adsorption increased with the increasing aluminum content in zeolite. The UV-Visible spectroscopy study showed that the spectra of tetracycline changed upon the interaction with zeolite beta, which could be ascribed to the formation of complexes of tetracycline and aluminum atoms in the zeolite surface. Nuclear magnetic resonance spectroscopy study further confirmed the participation of Al in the tetracycline adsorption. Fourier transform infrared spectroscopy studies showed that the amino functional groups in tetracycline were involved in the complexation with the zeolite surface. Copyright © 2010 Elsevier Inc. All rights reserved.

Cd(II) removal on surface-modified activated carbon: equilibrium, kinetics and mechanism.

PubMed

Liang, Jianjun; Liu, Meiling; Zhang, Yufei

2016-10-01

Commercial pulverous activated carbon (AC-0) was modified through two steps: oxidize AC-0 acid firstly, impregnate it with iron using ferric chloride secondly. Orthogonal experiment was conducted then to prepare modified activated carbon with high Cd(II) adsorption capacity (ACNF). Batch adsorption experiments were undertaken to determine the adsorption characteristics of Cd(II) from aqueous solution onto AC-0 and ACNF and the effect of pH, contact time and initial Cd(II) concentration. The results indicate that: the adsorption behavior of Cd(II) on ACNF can be well fitted with Langmuir model, and the maximum adsorption capacity of ACNF was 2.3 times higher than that of AC-0, supporting a monolayer coverage of Cd(II) on the surface. The kinetics of the adsorption process can be described by pseudo-second-order rate equation very well, and the adsorption capacity increased from 0.810 mg/g to 0.960 mg/g after modification. Compared with AC-0, the kinetic parameters of ACNF showed a higher adsorption rate through the aqueous solution to the solid surface and a lower intraparticle diffusion rate. Surface modification resulted in a lower Brunauer-Emmett-Teller (BET) surface area and pore size because of the collapse and blockage of pores, according to the X-ray diffraction (XRD) analysis, while the total number of surface oxygen acid groups increased, and this was supposed to contribute to the enhanced adsorption capacity of modified activated carbon.

Investigate the ultrasound energy assisted adsorption mechanism of nickel(II) ions onto modified magnetic cobalt ferrite nanoparticles: Multivariate optimization.

PubMed

Mehrabi, Fatemeh; Alipanahpour Dil, Ebrahim

2017-07-01

In present study, magnetic cobalt ferrite nanoparticles modified with (E)-N-(2-nitrobenzylidene)-2-(2-(2-nitrophenyl)imidazolidine-1-yl) ethaneamine (CoFe 2 O 4 -NPs-NBNPIEA) was synthesized and applied as novel adsorbent for ultrasound energy assisted adsorption of nickel(II) ions (Ni 2+ ) from aqueous solution. The prepared adsorbent characterized by Fourier transforms infrared spectroscopy (FT-IR), transmission electron microscope (TEM), vibrating sample magnetometer (VSM) and X-ray diffraction (XRD). The dependency of adsorption percentage to variables such as pH, initial Ni 2+ ions concentration, adsorbent mass and ultrasound time were studied with response surface methodology (RSM) by considering the desirable functions. The quadratic model between the dependent and independent variables was built. The proposed method showed good agreement between the experimental data and predictive value, and it has been successfully employed to adsorption of Ni 2+ ions from aqueous solution. Subsequently, the experimental equilibrium data at different concentration of Ni 2+ ions and 10mg amount of adsorbent mass was fitted to conventional isotherm models like Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich and it was revealed that the Langmuir is best model for explanation of behavior of experimental data. In addition, conventional kinetic models such as pseudo-first and second-order, Elovich and intraparticle diffusion were applied and it was seen that pseudo-second-order equation is suitable to fit the experimental data. Copyright © 2016 Elsevier B.V. All rights reserved.

Some Properties of the Fractional Equation of Continuity and the Fractional Diffusion Equation

NASA Astrophysics Data System (ADS)

Fukunaga, Masataka

2006-05-01

The fractional equation of continuity (FEC) and the fractional diffusion equation (FDE) show peculiar behaviors that are in the opposite sense to those expected from the equation of continuity and the diffusion equation, respectively. The behaviors are interpreted in terms of the memory effect of the fractional time derivatives included in the equations. Some examples are given by solutions of the FDE.

Solution of a modified fractional diffusion equation

NASA Astrophysics Data System (ADS)

Langlands, T. A. M.

2006-07-01

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein's brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259279; I.M. Sokolov, A.V. Checkin, J. Klafter, Distributed-order fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires an infinite series of Fox functions instead of a single Fox function.

Lattice Boltzmann simulation of the gas-solid adsorption process in reconstructed random porous media.

PubMed

Zhou, L; Qu, Z G; Ding, T; Miao, J Y

2016-04-01

The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.

Lattice Boltzmann simulation of the gas-solid adsorption process in reconstructed random porous media

NASA Astrophysics Data System (ADS)

Zhou, L.; Qu, Z. G.; Ding, T.; Miao, J. Y.

2016-04-01

The gas-solid adsorption process in reconstructed random porous media is numerically studied with the lattice Boltzmann (LB) method at the pore scale with consideration of interparticle, interfacial, and intraparticle mass transfer performances. Adsorbent structures are reconstructed in two dimensions by employing the quartet structure generation set approach. To implement boundary conditions accurately, all the porous interfacial nodes are recognized and classified into 14 types using a proposed universal program called the boundary recognition and classification program. The multiple-relaxation-time LB model and single-relaxation-time LB model are adopted to simulate flow and mass transport, respectively. The interparticle, interfacial, and intraparticle mass transfer capacities are evaluated with the permeability factor and interparticle transfer coefficient, Langmuir adsorption kinetics, and the solid diffusion model, respectively. Adsorption processes are performed in two groups of adsorbent media with different porosities and particle sizes. External and internal mass transfer resistances govern the adsorption system. A large porosity leads to an early time for adsorption equilibrium because of the controlling factor of external resistance. External and internal resistances are dominant at small and large particle sizes, respectively. Particle size, under which the total resistance is minimum, ranges from 3 to 7 μm with the preset parameters. Pore-scale simulation clearly explains the effect of both external and internal mass transfer resistances. The present paper provides both theoretical and practical guidance for the design and optimization of adsorption systems.

Diffusion Coefficients from Molecular Dynamics Simulations in Binary and Ternary Mixtures

NASA Astrophysics Data System (ADS)

Liu, Xin; Schnell, Sondre K.; Simon, Jean-Marc; Krüger, Peter; Bedeaux, Dick; Kjelstrup, Signe; Bardow, André; Vlugt, Thijs J. H.

2013-07-01

Multicomponent diffusion in liquids is ubiquitous in (bio)chemical processes. It has gained considerable and increasing interest as it is often the rate limiting step in a process. In this paper, we review methods for calculating diffusion coefficients from molecular simulation and predictive engineering models. The main achievements of our research during the past years can be summarized as follows: (1) we introduced a consistent method for computing Fick diffusion coefficients using equilibrium molecular dynamics simulations; (2) we developed a multicomponent Darken equation for the description of the concentration dependence of Maxwell-Stefan diffusivities. In the case of infinite dilution, the multicomponent Darken equation provides an expression for [InlineEquation not available: see fulltext.] which can be used to parametrize the generalized Vignes equation; and (3) a predictive model for self-diffusivities was proposed for the parametrization of the multicomponent Darken equation. This equation accurately describes the concentration dependence of self-diffusivities in weakly associating systems. With these methods, a sound framework for the prediction of mutual diffusion in liquids is achieved.

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

PubMed

Vlad, Marcel Ovidiu; Ross, John

2002-12-01

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

The role of fractional time-derivative operators on anomalous diffusion

NASA Astrophysics Data System (ADS)

Tateishi, Angel A.; Ribeiro, Haroldo V.; Lenzi, Ervin K.

2017-10-01

The generalized diffusion equations with fractional order derivatives have shown be quite efficient to describe the diffusion in complex systems, with the advantage of producing exact expressions for the underlying diffusive properties. Recently, researchers have proposed different fractional-time operators (namely: the Caputo-Fabrizio and Atangana-Baleanu) which, differently from the well-known Riemann-Liouville operator, are defined by non-singular memory kernels. Here we proposed to use these new operators to generalize the usual diffusion equation. By analyzing the corresponding fractional diffusion equations within the continuous time random walk framework, we obtained waiting time distributions characterized by exponential, stretched exponential, and power-law functions, as well as a crossover between two behaviors. For the mean square displacement, we found crossovers between usual and confined diffusion, and between usual and sub-diffusion. We obtained the exact expressions for the probability distributions, where non-Gaussian and stationary distributions emerged. This former feature is remarkable because the fractional diffusion equation is solved without external forces and subjected to the free diffusion boundary conditions. We have further shown that these new fractional diffusion equations are related to diffusive processes with stochastic resetting, and to fractional diffusion equations with derivatives of distributed order. Thus, our results suggest that these new operators may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.

Removal of anionic dye Congo red from aqueous solution by raw pine and acid-treated pine cone powder as adsorbent: equilibrium, thermodynamic, kinetics, mechanism and process design.

PubMed

Dawood, Sara; Sen, Tushar Kanti

2012-04-15

Pine cone a natural, low-cost agricultural by-product in Australia has been studied for its potential application as an adsorbent in its raw and hydrochloric acid modified form. Surface study of pine cone and treated pine cone was investigated using Fourier transform infrared (FTIR) and scanning electron microscopy (SEM). The modification process leads to increases in the specific surface area and decreases mean particle sizes of acid-treated pine cone when compared to raw pine cone biomass. Batch adsorption experiments were performed to remove anionic dye Congo red from aqueous solution. It was found that the extent of Congo red adsorption by both raw pine cone biomass and acid-treated biomass increased with initial dye concentration, contact time, temperature but decreased with increasing solution pH and amount of adsorbent of the system. Overall, kinetic studies showed that the dye adsorption process followed pseudo-second-order kinetics based on pseudo-first-order and intra-particle diffusion models. The different kinetic parameters including rate constant, half-adsorption time, and diffusion coefficient were determined at different physico-chemical conditions. Equilibrium data were best represented by Freundlich isotherm model among Langmuir and Freundlich adsorption isotherm models. It was observed that the adsorption was pH dependent and the maximum adsorption of 32.65 mg/g occurred at pH of 3.55 for an initial dye concentration of 20 ppm by raw pine cone, whereas for acid-treated pine cone the maximum adsorption of 40.19 mg/g for the same experimental conditions. Freundlich constant 'n' also indicated favourable adsorption. Thermodynamic parameters such as ∆G(0), ∆H(0), and ∆S(0) were calculated. A single-stage batch absorber design for the Congo red adsorption onto pine cone biomass also presented based on the Freundlich isotherm model equation. Copyright © 2012 Elsevier Ltd. All rights reserved.

Instability of turing patterns in reaction-diffusion-ODE systems.

PubMed

Marciniak-Czochra, Anna; Karch, Grzegorz; Suzuki, Kanako

2017-02-01

The aim of this paper is to contribute to the understanding of the pattern formation phenomenon in reaction-diffusion equations coupled with ordinary differential equations. Such systems of equations arise, for example, from modeling of interactions between cellular processes such as cell growth, differentiation or transformation and diffusing signaling factors. We focus on stability analysis of solutions of a prototype model consisting of a single reaction-diffusion equation coupled to an ordinary differential equation. We show that such systems are very different from classical reaction-diffusion models. They exhibit diffusion-driven instability (turing instability) under a condition of autocatalysis of non-diffusing component. However, the same mechanism which destabilizes constant solutions of such models, destabilizes also all continuous spatially heterogeneous stationary solutions, and consequently, there exist no stable Turing patterns in such reaction-diffusion-ODE systems. We provide a rigorous result on the nonlinear instability, which involves the analysis of a continuous spectrum of a linear operator induced by the lack of diffusion in the destabilizing equation. These results are extended to discontinuous patterns for a class of nonlinearities.

Background-Error Correlation Model Based on the Implicit Solution of a Diffusion Equation

DTIC Science & Technology

2010-01-01

1 Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation Matthew J. Carrier* and Hans Ngodock...4. TITLE AND SUBTITLE Background- Error Correlation Model Based on the Implicit Solution of a Diffusion Equation 5a. CONTRACT NUMBER 5b. GRANT...2001), which sought to model error correlations based on the explicit solution of a generalized diffusion equation. The implicit solution is

Adsorption of ammonium ion by coconut shell-activated carbon from aqueous solution: kinetic, isotherm, and thermodynamic studies.

PubMed

Boopathy, Ramasamy; Karthikeyan, Sekar; Mandal, Asit Baran; Sekaran, Ganesan

2013-01-01

Ammonium ions are one of the most encountered nitrogen species in polluted water bodies. High level of ammonium ion in aqueous solution imparts unpleasant taste and odor problems, which can interfere with the life of aquatics and human population when discharged. Many chemical methods are developed and being used for removal of ammonium ion from aqueous solution. Among various techniques, adsorption was found to be the most feasible and environmentally friendly with the use of natural-activated adsorbents. Hence, in this study, coconut shell-activated carbon (CSAC) was prepared and used for the removal of ammonium ion by adsorption techniques. Ammonium chloride (analytical grade) was purchased from Merck Chemicals for adsorption studies. The CSAC was used to adsorb ammonium ions under stirring at 100 rpm, using orbital shaker in batch experiments. The concentration of ammonium ion was estimated by ammonia distillate, using a Buchi distillation unit. The influence of process parameters such as pH, temperature, and contact time was studied for adsorption of ammonium ion, and kinetic, isotherm models were validated to understand the mechanism of adsorption of ammonium ion by CSAC. Thermodynamic properties such as ∆G, ∆H, and ∆S were determined for the ammonium adsorption, using van't Hoff equation. Further, the adsorption of ammonium ion was confirmed through instrumental analyses such as SEM, XRD, and FTIR. The optimum conditions for the effective adsorption of ammonium ion onto CSAC were found to be pH 9.0, temperature 283 K, and contact time 120 min. The experimental data was best followed by pseudosecond order equation, and the adsorption isotherm model obeyed the Freundlich isotherm. This explains the ammonium ion adsorption onto CSAC which was a multilayer adsorption with intraparticle diffusion. Negative enthalpy confirmed that this adsorption process was exothermic. The instrumental analyses confirmed the adsorption of ammonium ion onto CSAC.

Diffusion of Charged Species in Liquids

NASA Astrophysics Data System (ADS)

Del Río, J. A.; Whitaker, S.

2016-11-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids.

PubMed

Del Río, J A; Whitaker, S

2016-11-04

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases.

Diffusion of Charged Species in Liquids

PubMed Central

del Río, J. A.; Whitaker, S.

2016-01-01

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three dominant forces: (a) the gradient of the partial pressure, (b) the electrostatic force, and (c) the diffusive drag force that is a central feature of the Maxwell-Stefan equations. For ideal gas mixtures we derive the classic Nernst-Planck equation. For liquid-phase diffusion we encounter a situation in which the Nernst-Planck contribution to diffusion differs by several orders of magnitude from that obtained for ideal gases. PMID:27811959

Fabrication of the novel hydrogel based on waste corn stalk for removal of methylene blue dye from aqueous solution

NASA Astrophysics Data System (ADS)

Ma, Dongzhuo; Zhu, Baodong; Cao, Bo; Wang, Jian; Zhang, Jianwei

2017-11-01

The novel hydrogel based on waste corn stalk was synthetized by aqueous solution polymerization technique with functional monomers in the presence of organic montmorillonite (OMMT) under ultrasonic. In this study, batch adsorption experiments were carried out to research the effect of initial dye concentration, the dosage of hydrogel, stirring speed, contact time and temperature on the adsorption of methylene blue (MB) dye. The adsorption process was best described by the pseudo-second-order kinetic model, which confirmed that it should be a chemical process. Furthermore, we ascertained the rate controlling step by establishing the intraparticle diffusion model and the liquid film diffusion model. The adsorption and synthesis mechanisms were vividly depicted in our work as well. Structural and morphological characterizations by virtue of FTIR, FESEM, and Biomicroscope supported the relationship between the adsorption performance and material's microstructure. This research is a valuable contribution for the environmental protection, which not only converts waste corn stalks into functional materials, but improves the removal of organic dye from sewage water.

Removal of sulfur compounds from petroleum refinery wastewater through adsorption on modified activated carbon.

PubMed

Ben Hariz, Ichrak; Al Ayni, Foued; Monser, Lotfi

2014-01-01

The adsorption of sulfur compounds from petroleum refinery wastewater on a chemically modified activated carbon (MAC) was investigated. The modification technique (nitric acid, hydrogen peroxide and thermal modification) enhanced the removal capacity of carbon and therefore decreases cost-effective removal of sulfide from refinery wastewater. Adsorption equilibrium and kinetics data were determined for sulfur removal from real refinery wastewater. The data were evaluated according to several adsorption isotherm and kinetics models. The Freundlich isotherm fitted well with the equilibrium data of sulfur on different adsorbents, whereas the kinetics data were best fitted by the pseudo-second-order model. Insights of sulfide removal mechanisms indicated that the sorption was controlled through the intraparticle diffusion mechanism with a significant contribution of film diffusion. The MAC adsorbent was found to have an effective removal capacity of approximately 2.5 times that of non-modified carbon. Using different MAC, sulfides were eliminated with a removal capacity of 52 mg g(-1). Therefore, MAC can be utilized as an effective and less expensive adsorbent for the reduction of sulfur in refinery wastewater.

Microscopic Interpretation and Generalization of the Bloch-Torrey Equation for Diffusion Magnetic Resonance

PubMed Central

Seroussi, Inbar; Grebenkov, Denis S.; Pasternak, Ofer; Sochen, Nir

2017-01-01

In order to bridge microscopic molecular motion with macroscopic diffusion MR signal in complex structures, we propose a general stochastic model for molecular motion in a magnetic field. The Fokker-Planck equation of this model governs the probability density function describing the diffusion-magnetization propagator. From the propagator we derive a generalized version of the Bloch-Torrey equation and the relation to the random phase approach. This derivation does not require assumptions such as a spatially constant diffusion coefficient, or ad-hoc selection of a propagator. In particular, the boundary conditions that implicitly incorporate the microstructure into the diffusion MR signal can now be included explicitly through a spatially varying diffusion coefficient. While our generalization is reduced to the conventional Bloch-Torrey equation for piecewise constant diffusion coefficients, it also predicts scenarios in which an additional term to the equation is required to fully describe the MR signal. PMID:28242566

Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps

NASA Astrophysics Data System (ADS)

Yi, Taishan; Chen, Yuming

2017-12-01

In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.

Kinetics of Microbial Reduction of Solid Phase U(VI)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Chongxuan; Jeon, Byong Hun; Zachara, John M.

2006-10-01

Sodium boltwoodite (NaUO2SiO3OH ?1.5H2O) was used to assess the kinetics of microbial reduction of solid phase U(VI) by a dissimilatory metal-reducing bacterium (DMRB), Shewanella oneidensis strain MR-1. The bioreduction kinetics was studied with Na-boltwoodite in suspension or within alginate beads. Concentrations of U(VI)tot and cell number were varied to evaluate the coupling of U(VI) dissolution, diffusion, and microbial activity. Batch experiments were performed in a non-growth medium with lactate as electron donor at pH 6.8 buffered with PIPES. Microscopic and spectroscopic analyses with transmission electron microscopy (TEM), energy dispersive spectroscopy (EDS), and laser-induced fluorescence spectroscopy (LIFS) collectively indicated that solidmore » phase U(VI) was first dissolved and diffused out of grain interiors before it was reduced on bacterial surfaces and/or within the periplasm. The kinetics of solid phase U(VI) bioreduction was well described by a coupled model of bicarbonate-promoted dissolution of Na-boltwoodite, intraparticle uranyl diffusion, and Monod type bioreduction kinetics with respect to dissolved U(VI) concentration. The results demonstrated the intimate coupling of biological, chemical, and physical processes in microbial reduction of solid phase U(VI).« less

Prediction of stream volatilization coefficients

USGS Publications Warehouse

Rathbun, Ronald E.

1990-01-01

Equations are developed for predicting the liquid-film and gas-film reference-substance parameters for quantifying volatilization of organic solutes from streams. Molecular weight and molecular-diffusion coefficients of the solute are used as correlating parameters. Equations for predicting molecular-diffusion coefficients of organic solutes in water and air are developed, with molecular weight and molal volume as parameters. Mean absolute errors of prediction for diffusion coefficients in water are 9.97% for the molecular-weight equation, 6.45% for the molal-volume equation. The mean absolute error for the diffusion coefficient in air is 5.79% for the molal-volume equation. Molecular weight is not a satisfactory correlating parameter for diffusion in air because two equations are necessary to describe the values in the data set. The best predictive equation for the liquid-film reference-substance parameter has a mean absolute error of 5.74%, with molal volume as the correlating parameter. The best equation for the gas-film parameter has a mean absolute error of 7.80%, with molecular weight as the correlating parameter.

Causal Diffusion and the Survival of Charge Fluctuations

NASA Astrophysics Data System (ADS)

Abdel-Aziz, Mohamed; Gavin, Sean

2004-10-01

Diffusion may obliterate fluctuation signals of the QCD phase transition in nuclear collisions at SPS and RHIC energies. We propose a hyperbolic diffusion equation to study the dissipation of net charge fluctuations [1]. This equation is needed in a relativistic context, because the classic parabolic diffusion equation violates causality. We find that causality substantially limits the extent to which diffusion can dissipate these fluctuations. [1] M. Abdel-Aziz and S. Gavin, nucl-th/0404058

Hybrid molecularly imprinted poly(methacrylic acid-TRIM)-silica chemically modified with (3-glycidyloxypropyl)trimethoxysilane for the extraction of folic acid in aqueous medium.

PubMed

de Oliveira, Fernanda Midori; Segatelli, Mariana Gava; Tarley, César Ricardo Teixeira

2016-02-01

In the present study a hybrid molecularly imprinted poly(methacrylic acid-trimethylolpropane trimethacrylate)-silica (MIP) was synthesized and modified with (3-glycidyloxypropyl)trimethoxysilane (GPTMS) with posterior opening of epoxy ring to provide hydrophilic properties of material in the extraction of folic acid from aqueous medium. The chemical and structural aggregates of hybrid material were characterized by means of Fourier Transform Infrared (FT-IR), Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), Thermogravimetric analysis (TGA) and textural data. Selectivity data of MIP were compared to non-imprinted polymer (NIP) through competitive sorption studies in the presence of caffeine, paracetamol or 4-aminobenzamide yielding relative selectivity coefficients (k′) higher than one unit, thus confirming the selective character of MIP even in the presence of structurally smaller compounds than the folic acid. The lower hydrophobic sorption by bovine serum albumin (BSA) in the MIP as compared to unmodified MIP proves the hydrophilicity of polymer surface by using GPTMS with opening ring. Under acid medium(pH 1.5) the sorption of folic acid onto MIP from batch experiments was higher than the one achieved for NIP. Equilibrium sorption of folic acid was reached at 120 min for MIP, NIP and MIP without GPTMS and kinetic sorption data were well described by pseudo-second-order, Elovich and intraparticle diffusion models. Thus, these results indicate the existence of different binding energy sites in the polymers and a complex mechanism consisting of both surface sorption and intraparticle transport of folic acid within the pores of polymers.

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

NASA Astrophysics Data System (ADS)

Hu, Wenjie; Duan, Yueliang

2018-04-01

We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.

FRACTIONAL PEARSON DIFFUSIONS.

PubMed

Leonenko, Nikolai N; Meerschaert, Mark M; Sikorskii, Alla

2013-07-15

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding time-fractional diffusion equation. They are useful for modeling sub-diffusive phenomena, caused by particle sticking and trapping. This paper provides explicit strong solutions for fractional Pearson diffusions, using spectral methods. It also presents stochastic solutions, using a non-Markovian inverse stable time change.

A nonlinear equation for ionic diffusion in a strong binary electrolyte

PubMed Central

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

An Ab Initio and Kinetic Monte Carlo Simulation Study of Lithium Ion Diffusion on Graphene

PubMed Central

Zhong, Kehua; Yang, Yanmin; Xu, Guigui; Zhang, Jian-Min; Huang, Zhigao

2017-01-01

The Li+ diffusion coefficients in Li+-adsorbed graphene systems were determined by combining first-principle calculations based on density functional theory with Kinetic Monte Carlo simulations. The calculated results indicate that the interactions between Li ions have a very important influence on lithium diffusion. Based on energy barriers directly obtained from first-principle calculations for single-Li+ and two-Li+ adsorbed systems, a new equation predicting energy barriers with more than two Li ions was deduced. Furthermore, it is found that the temperature dependence of Li+ diffusion coefficients fits well to the Arrhenius equation, rather than meeting the equation from electrochemical impedance spectroscopy applied to estimate experimental diffusion coefficients. Moreover, the calculated results also reveal that Li+ concentration dependence of diffusion coefficients roughly fits to the equation from electrochemical impedance spectroscopy in a low concentration region; however, it seriously deviates from the equation in a high concentration region. So, the equation from electrochemical impedance spectroscopy technique could not be simply used to estimate the Li+ diffusion coefficient for all Li+-adsorbed graphene systems with various Li+ concentrations. Our work suggests that interactions between Li ions, and among Li ion and host atoms will influence the Li+ diffusion, which determines that the Li+ intercalation dependence of Li+ diffusion coefficient should be changed and complex. PMID:28773122

Diffusion equations and the time evolution of foreign exchange rates

NASA Astrophysics Data System (ADS)

Figueiredo, Annibal; de Castro, Marcio T.; da Fonseca, Regina C. B.; Gleria, Iram

2013-10-01

We investigate which type of diffusion equation is most appropriate to describe the time evolution of foreign exchange rates. We modify the geometric diffusion model assuming a non-exponential time evolution and the stochastic term is the sum of a Wiener noise and a jump process. We find the resulting diffusion equation to obey the Kramers-Moyal equation. Analytical solutions are obtained using the characteristic function formalism and compared with empirical data. The analysis focus on the first four central moments considering the returns of foreign exchange rate. It is shown that the proposed model offers a good improvement over the classical geometric diffusion model.

Removal of fluoride by thermally activated carbon prepared from neem (Azadirachta indica) and kikar (Acacia arabica) leaves.

PubMed

Kumar, Sunil; Gupta, Asha; Yadav, J P

2008-03-01

The present investigation deals with fluoride removal from aqueous solution by thermally activated neem (Azadirachta indica) leaves carbon (ANC) and thermally activated kikar (Acacia arabica) leaves carbon (AKC) adsorbents. In this study neem leaves carbon and kikar leaves carbon prepared by heating the leaves at 400 degrees C in electric furnace was found to be useful for the removal of fluoride. The adsorbents of 0.3 mm and 1.0 mm sizes of neem and kikar leaves carbon was prepared by standard sieve. Batch experiments done to see the fluoride removal properties from synthetic solution of 5 ppm to study the influence of pH, adsorbent dose and contact time on adsorption efficiency The optimum pH was found to be 6 for both adsorbents. The optimum dose was found to be 0.5g/100 ml forANC (activated neem leaves carbon) and 0.7g/100 ml forAKC (activated kikar leaves carbon). The optimum time was found to be one hour for both the adsorbent. It was also found that adsorbent size of 0.3 mm was more efficient than the 1.0 mm size. The adsorption process obeyed Freundlich adsorption isotherm. The straight line of log (qe-q) vs time at ambient temperature indicated the validity of langergren equation consequently first order nature of the process involved in the present study. Results indicate that besides intraparticle diffusion there maybe other processes controlling the rate which may be operating simultaneously. All optimized conditions were applied for removal of fluoride from four natural water samples.

Microwave-assisted synthesis of carbon supported metal/metal oxide nanocomposites and their application in water purification

NASA Astrophysics Data System (ADS)

Gunawan, Gunawan

A novel, easy, and cost effective method for synthesizing carbon supported metal/metal oxide nanocomposites has been studied. Carbon supported metal/metal oxide nanocomposites have niche applications in the area of catalysis, fuel cells, electrodes, and more. The method utilizes a commercial microwave and features the addition of a developed graphite-jacket technique with renewable carbon resources, tannin and lignin. The method has been successfully used to synthesize carbon/nickel, carbon/iron oxide, and carbon/nickel phosphide nanocomposites. The method has shown its versatility in the synthesis of carbon nanocomposites. The process is much simpler when compared with the available methods for synthesizing carbon nanocomposites. The synthesized nanocomposites were classified using several characterization techniques, such as electron microscopy, X-ray powder diffraction, surface area analysis, thermogravimetric analysis, and spectrophotometric studies. One application of the carbon nanocomposite is in wastewater remediation. The synthesized carbon/iron oxide nanocomposite was noted as being useful for removing arsenic (As) and phosphorus (P) from contaminated water. The adsorption process of the nanocomposite was critically studied in order to understand the process of removing pollutants from contaminated water. The study shows that the nanocomposites are capable of removing As and P from contaminated water. Kinetic and adsorption isotherm studies were applied to understand the adsorption of As and P onto the adsorbent. Several methods, such as pseudo-first and second order kinetic models, Elovich's equation, and the Weber-Morris intraparticle diffusion model were used to explain the kinetic aspects of the adsorption process. For the adsorption isotherm study, Langmuir and Freundlich isotherm models were applied.

Kinetic and thermodynamic studies of the Co(II) and Ni(II) ions removal from aqueous solutions by Ca-Mg phosphates.

PubMed

Ivanets, A I; Srivastava, V; Kitikova, N V; Shashkova, I L; Sillanpää, M

2017-03-01

The aim of this work was to study the sorption kinetics and thermodynamics of Co(II) and Ni(II) from aqueous solutions by sorbents on the basis of hydrogen (PD-1) and tertiary (PD-2) Ca-Mg phosphates depending on the solution temperature and sorbents chemical composition. Kinetic studies of adsorption of Co(II) and Ni(II) ions onto samples of phosphate sorbents were performed in batch experiment at the temperatures 288, 303, 318 and 333 K. The sorbent dose was fixed at 10 g L -1 , initial pH value 2.6, and contact time varied from 5 to 600 min. The kinetics of Co(II) and Ni(II) adsorption were analyzed by using pseudo-first order, pseudo-second order and intraparticle diffusion models. Thermodynamic parameters (ΔG°, ΔH° and ΔS°) for the sorption of Co(II) and Ni(II) were determined using the Gibbs-Helmholtz equation. The calculated kinetic parameters and corresponding correlation coefficients revealed that Co(II) and Ni(II) uptake process followed the pseudo-second order rate expression. Thermodynamic studies confirmed the spontaneous and endothermic nature of removal process which indicate that sorption of Co(II) and Ni(II) ions onto both phosphate sorbents is favoured at higher temperatures and has the chemisorptive mechanism. The data thus obtained would be useful for practical application of the low cost and highly effective Ca-Mg phosphate sorbents. Copyright © 2016 Elsevier Ltd. All rights reserved.

The exit-time problem for a Markov jump process

NASA Astrophysics Data System (ADS)

Burch, N.; D'Elia, M.; Lehoucq, R. B.

2014-12-01

The purpose of this paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developed nonlocal vector calculus. This calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.

Effects of curved midline and varying width on the description of the effective diffusivity of Brownian particles

NASA Astrophysics Data System (ADS)

Chávez, Yoshua; Chacón-Acosta, Guillermo; Dagdug, Leonardo

2018-05-01

Axial diffusion in channels and tubes of smoothly-varying geometry can be approximately described as one-dimensional diffusion in the entropy potential with a position-dependent effective diffusion coefficient, by means of the modified Fick–Jacobs equation. In this work, we derive analytical expressions for the position-dependent effective diffusivity for two-dimensional asymmetric varying-width channels, and for three-dimensional curved midline tubes, formed by straight walls. To this end, we use a recently developed theoretical framework using the Frenet–Serret moving frame as the coordinate system (2016 J. Chem. Phys. 145 074105). For narrow tubes and channels, an effective one-dimensional description reducing the diffusion equation to a Fick–Jacobs-like equation in general coordinates is used. From this last equation, one can calculate the effective diffusion coefficient applying Neumann boundary conditions.

General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-05-01

Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 < α , β ≤ 2 } based on the fractional derivative, has not been obtained, where α and β are time and space derivative orders. It is essential to derive a general PFG signal attenuation expression including the FGPW effect for PFG anisotropic anomalous diffusion research. In this paper, two recently developed modified-Bloch equations, the fractal differential modified-Bloch equation and the fractional integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

A parallel algorithm for nonlinear convection-diffusion equations

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.

1990-01-01

A parallel algorithm for the efficient solution of nonlinear time-dependent convection-diffusion equations with small parameter on the diffusion term is presented. The method is based on a physically motivated domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. The method is suitable for the solution of problems arising in the simulation of fluid dynamics. Experimental results for a nonlinear equation in two-dimensions are presented.

The time-fractional radiative transport equation—Continuous-time random walk, diffusion approximation, and Legendre-polynomial expansion

NASA Astrophysics Data System (ADS)

Machida, Manabu

2017-01-01

We consider the radiative transport equation in which the time derivative is replaced by the Caputo derivative. Such fractional-order derivatives are related to anomalous transport and anomalous diffusion. In this paper we describe how the time-fractional radiative transport equation is obtained from continuous-time random walk and see how the equation is related to the time-fractional diffusion equation in the asymptotic limit. Then we solve the equation with Legendre-polynomial expansion.

Generalized fractional diffusion equations for accelerating subdiffusion and truncated Lévy flights

NASA Astrophysics Data System (ADS)

Chechkin, A. V.; Gonchar, V. Yu.; Gorenflo, R.; Korabel, N.; Sokolov, I. M.

2008-08-01

Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by diffusion equations with fractional derivatives of distributed order. Such equations were introduced in A. V. Chechkin, R. Gorenflo, and I. Sokolov [Phys. Rev. E 66, 046129 (2002)] for the description of the processes getting more anomalous in the course of time (decelerating subdiffusion and accelerating superdiffusion). Here we discuss the properties of diffusion equations with fractional derivatives of the distributed order for the description of anomalous relaxation and diffusion phenomena getting less anomalous in the course of time, which we call, respectively, accelerating subdiffusion and decelerating superdiffusion. For the former process, by taking a relatively simple particular example with two fixed anomalous diffusion exponents we show that the proposed equation effectively describes the subdiffusion phenomenon with diffusion exponent varying in time. For the latter process we demonstrate by a particular example how the power-law truncated Lévy stable distribution evolves in time to the distribution with power-law asymptotics and Gaussian shape in the central part. The special case of two different orders is characteristic for the general situation in which the extreme orders dominate the asymptotics.

Symmetry classification of time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Naeem, I.; Khan, M. D.

2017-01-01

In this article, a new approach is proposed to construct the symmetry groups for a class of fractional differential equations which are expressed in the modified Riemann-Liouville fractional derivative. We perform a complete group classification of a nonlinear fractional diffusion equation which arises in fractals, acoustics, control theory, signal processing and many other applications. Introducing the suitable transformations, the fractional derivatives are converted to integer order derivatives and in consequence the nonlinear fractional diffusion equation transforms to a partial differential equation (PDE). Then the Lie symmetries are computed for resulting PDE and using inverse transformations, we derive the symmetries for fractional diffusion equation. All cases are discussed in detail and results for symmetry properties are compared for different values of α. This study provides a new way of computing symmetries for a class of fractional differential equations.

Heavy-tailed fractional Pearson diffusions.

PubMed

Leonenko, N N; Papić, I; Sikorskii, A; Šuvak, N

2017-11-01

We define heavy-tailed fractional reciprocal gamma and Fisher-Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions. Pearson diffusions are governed by the backward Kolmogorov equations with space-varying polynomial coefficients and are widely used in applications. The corresponding fractional reciprocal gamma and Fisher-Snedecor diffusions are governed by the fractional backward Kolmogorov equations and have heavy-tailed marginal distributions in the steady state. We derive the explicit expressions for the transition densities of the fractional reciprocal gamma and Fisher-Snedecor diffusions and strong solutions of the associated Cauchy problems for the fractional backward Kolmogorov equation.

Uranium biosorption by Padina sp. algae biomass: kinetics and thermodynamics.

PubMed

Khani, Mohammad Hassan

2011-11-01

Kinetic, thermodynamic, and equilibrium isotherms of the biosorption of uranium ions onto Padina sp., a brown algae biomass, in a batch system have been studied. The kinetic data were found to follow the pseudo-second-order model. Intraparticle diffusion is not the sole rate-controlling factor. The equilibrium experimental results were analyzed in terms of Langmuir isotherm depending with temperature. Equilibrium data fitted very well to the Langmuir model. The maximum uptakes estimated by using the Langmuir model were 434.8, 416.7, 400.0, and 370.4 mg/g at 10°C, 20°C, 30°C, and 40°C, respectively. Gibbs free energy was spontaneous for all interactions, and the adsorption process exhibited exothermic enthalpy values. Padina sp. algae were shown to be a favorable biosorbent for uranium removal from aqueous solutions.

Intraparticle FRET for Enhanced Efficiency of Two-Photon Activated Photodynamic Therapy.

PubMed

Cao, Hongqian; Yang, Yang; Qi, Yanfei; Li, Yue; Sun, Bingbing; Li, Ying; Cui, Wei; Li, Juan; Li, Junbai

2018-06-01

Photodynamic therapy (PDT) still faces two main problems on cancer therapy. One is how to improve PDT efficiency against hypoxic environment of tumors. The other one is how to overcome the limit of short wavelength light to increase PDT treatment depth. In this work, an intraparticle fluorescence resonance energy transfer (FRET) platform is designed to address these problems together. The nanoparticles are doped with multicomponents, such as catalase, two-photon dyes, and traditional photosensitizers, with a simple "one-pot" and green method. On the one hand, catalase can catalyze intracellular H 2 O 2 into O 2 and promote PDT efficiency. One the other hand, photosensitizers can be excited indirectly by two-photon lasers through an intraparticle FRET mechanism, which results in deeper tissue penetration for PDT. These properties are verified through the material induced cytotoxicity in light or in dark and in vivo blocking blood-vessel experiment. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Controlling photophysical properties of ultrasmall conjugated polymer nanoparticles through polymer chain packing

PubMed Central

Piwoński, Hubert; Michinobu, Tsuyoshi; Habuchi, Satoshi

2017-01-01

Applications of conjugated polymer nanoparticles (Pdots) for imaging and sensing depend on their size, fluorescence brightness and intraparticle energy transfer. The molecular design of conjugated polymers (CPs) has been the main focus of the development of Pdots. Here we demonstrate that proper control of the physical interactions between the chains is as critical as the molecular design. The unique design of twisted CPs and fine-tuning of the reprecipitation conditions allow us to fabricate ultrasmall (3.0–4.5 nm) Pdots with excellent photostability. Extensive photophysical and structural characterization reveals the essential role played by the packing of the polymer chains in the particles in the intraparticle spatial alignment of the emitting sites, which regulate the fluorescence brightness and the intraparticle energy migration efficiency. Our findings enhance understanding of the relationship between chain interactions and the photophysical properties of CP nanomaterials, providing a framework for designing and fabricating functional Pdots for imaging applications. PMID:28508857

Feynman-Kac equations for reaction and diffusion processes

NASA Astrophysics Data System (ADS)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

NASA Astrophysics Data System (ADS)

Doha, Eid H.; Bhrawy, Ali H.; Ezz-Eldien, Samer S.

2013-10-01

In this paper, a class of fractional diffusion equations with variable coefficients is considered. An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically is proposed. This method is based upon Chebyshev tau approximation together with Chebyshev operational matrix of Caputo fractional differentiation. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. We apply this general method to solve four specific examples. In each of the examples considered, the numerical results show that the proposed method is of high accuracy and is efficient for solving the time-dependent fractional diffusion equations.

The exit-time problem for a Markov jump process

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burch, N.; D'Elia, Marta; Lehoucq, Richard B.

2014-12-15

The purpose of our paper is to consider the exit-time problem for a finite-range Markov jump process, i.e, the distance the particle can jump is bounded independent of its location. Such jump diffusions are expedient models for anomalous transport exhibiting super-diffusion or nonstandard normal diffusion. We refer to the associated deterministic equation as a volume-constrained nonlocal diffusion equation. The volume constraint is the nonlocal analogue of a boundary condition necessary to demonstrate that the nonlocal diffusion equation is well-posed and is consistent with the jump process. A critical aspect of the analysis is a variational formulation and a recently developedmore » nonlocal vector calculus. Furthermore, this calculus allows us to pose nonlocal backward and forward Kolmogorov equations, the former equation granting the various moments of the exit-time distribution.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

NASA Astrophysics Data System (ADS)

Horowitz, Jordan M.

2015-07-01

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium.

PubMed

Horowitz, Jordan M

2015-07-28

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochastic thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

NASA Astrophysics Data System (ADS)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Diffusion Influenced Adsorption Kinetics.

PubMed

Miura, Toshiaki; Seki, Kazuhiko

2015-08-27

When the kinetics of adsorption is influenced by the diffusive flow of solutes, the solute concentration at the surface is influenced by the surface coverage of solutes, which is given by the Langmuir-Hinshelwood adsorption equation. The diffusion equation with the boundary condition given by the Langmuir-Hinshelwood adsorption equation leads to the nonlinear integro-differential equation for the surface coverage. In this paper, we solved the nonlinear integro-differential equation using the Grünwald-Letnikov formula developed to solve fractional kinetics. Guided by the numerical results, analytical expressions for the upper and lower bounds of the exact numerical results were obtained. The upper and lower bounds were close to the exact numerical results in the diffusion- and reaction-controlled limits, respectively. We examined the validity of the two simple analytical expressions obtained in the diffusion-controlled limit. The results were generalized to include the effect of dispersive diffusion. We also investigated the effect of molecular rearrangement of anisotropic molecules on surface coverage.

Analytical solutions of the space-time fractional Telegraph and advection-diffusion equations

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Schlickeiser, Reinhard; Elhanbaly, A.

2018-02-01

The aim of this paper is to develop a fractional derivative model of energetic particle transport for both uniform and non-uniform large-scale magnetic field by studying the fractional Telegraph equation and the fractional advection-diffusion equation. Analytical solutions of the space-time fractional Telegraph equation and space-time fractional advection-diffusion equation are obtained by use of the Caputo fractional derivative and the Laplace-Fourier technique. The solutions are given in terms of Fox's H function. As an illustration they are applied to the case of solar energetic particles.

Boundary value problems for multi-term fractional differential equations

NASA Astrophysics Data System (ADS)

Daftardar-Gejji, Varsha; Bhalekar, Sachin

2008-09-01

Multi-term fractional diffusion-wave equation along with the homogeneous/non-homogeneous boundary conditions has been solved using the method of separation of variables. It is observed that, unlike in the one term case, solution of multi-term fractional diffusion-wave equation is not necessarily non-negative, and hence does not represent anomalous diffusion of any kind.

A finite element formulation preserving symmetric and banded diffusion stiffness matrix characteristics for fractional differential equations

NASA Astrophysics Data System (ADS)

Lin, Zeng; Wang, Dongdong

2017-10-01

Due to the nonlocal property of the fractional derivative, the finite element analysis of fractional diffusion equation often leads to a dense and non-symmetric stiffness matrix, in contrast to the conventional finite element formulation with a particularly desirable symmetric and banded stiffness matrix structure for the typical diffusion equation. This work first proposes a finite element formulation that preserves the symmetry and banded stiffness matrix characteristics for the fractional diffusion equation. The key point of the proposed formulation is the symmetric weak form construction through introducing a fractional weight function. It turns out that the stiffness part of the present formulation is identical to its counterpart of the finite element method for the conventional diffusion equation and thus the stiffness matrix formulation becomes trivial. Meanwhile, the fractional derivative effect in the discrete formulation is completely transferred to the force vector, which is obviously much easier and efficient to compute than the dense fractional derivative stiffness matrix. Subsequently, it is further shown that for the general fractional advection-diffusion-reaction equation, the symmetric and banded structure can also be maintained for the diffusion stiffness matrix, although the total stiffness matrix is not symmetric in this case. More importantly, it is demonstrated that under certain conditions this symmetric diffusion stiffness matrix formulation is capable of producing very favorable numerical solutions in comparison with the conventional non-symmetric diffusion stiffness matrix finite element formulation. The effectiveness of the proposed methodology is illustrated through a series of numerical examples.

Diffusion coefficients in organic-water solutions and comparison with Stokes-Einstein predictions

NASA Astrophysics Data System (ADS)

Evoy, E.; Kamal, S.; Bertram, A. K.

2017-12-01

Diffusion coefficients of organic species in particles containing secondary organic material (SOM) are necessary for predicting the growth and reactivity of these particles in the atmosphere. Previously, the Stokes-Einstein equation combined with viscosity measurements have been used to predict these diffusion coefficients. However, the accuracy of the Stokes-Einstein equation for predicting diffusion coefficients in SOM-water particles has not been quantified. To test the Stokes-Einstein equation, diffusion coefficients of fluorescent organic probe molecules were measured in citric acid-water and sorbitol-water solutions. These solutions were used as proxies for SOM-water particles found in the atmosphere. Measurements were performed as a function of water activity, ranging from 0.26-0.86, and as a function of viscosity ranging from 10-3 to 103 Pa s. Diffusion coefficients were measured using fluorescence recovery after photobleaching. The measured diffusion coefficients were compared with predictions made using the Stokes-Einstein equation combined with literature viscosity data. Within the uncertainties of the measurements, the measured diffusion coefficients agreed with the predicted diffusion coefficients, in all cases.

Diffusion approximations to the chemical master equation only have a consistent stochastic thermodynamics at chemical equilibrium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horowitz, Jordan M., E-mail: jordan.horowitz@umb.edu

The stochastic thermodynamics of a dilute, well-stirred mixture of chemically reacting species is built on the stochastic trajectories of reaction events obtained from the chemical master equation. However, when the molecular populations are large, the discrete chemical master equation can be approximated with a continuous diffusion process, like the chemical Langevin equation or low noise approximation. In this paper, we investigate to what extent these diffusion approximations inherit the stochastic thermodynamics of the chemical master equation. We find that a stochastic-thermodynamic description is only valid at a detailed-balanced, equilibrium steady state. Away from equilibrium, where there is no consistent stochasticmore » thermodynamics, we show that one can still use the diffusive solutions to approximate the underlying thermodynamics of the chemical master equation.« less

S{sub 2}SA preconditioning for the S{sub n} equations with strictly non negative spatial discretization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bruss, D. E.; Morel, J. E.; Ragusa, J. C.

2013-07-01

Preconditioners based upon sweeps and diffusion-synthetic acceleration have been constructed and applied to the zeroth and first spatial moments of the 1-D S{sub n} transport equation using a strictly non negative nonlinear spatial closure. Linear and nonlinear preconditioners have been analyzed. The effectiveness of various combinations of these preconditioners are compared. In one dimension, nonlinear sweep preconditioning is shown to be superior to linear sweep preconditioning, and DSA preconditioning using nonlinear sweeps in conjunction with a linear diffusion equation is found to be essentially equivalent to nonlinear sweeps in conjunction with a nonlinear diffusion equation. The ability to use amore » linear diffusion equation has important implications for preconditioning the S{sub n} equations with a strictly non negative spatial discretization in multiple dimensions. (authors)« less

Sorption reaction mechanism of some hazardous radionuclides from mixed waste by impregnated crown ether onto polymeric resin.

PubMed

Shehata, F A; Attallah, M F; Borai, E H; Hilal, M A; Abo-Aly, M M

2010-02-01

A novel impregnated polymeric resin was practically tested as adsorbent material for removal of some hazardous radionuclides from radioactive liquid waste. The applicability for the treatment of low-level liquid radioactive waste was investigated. The material was prepared by loading 4,4'(5')di-t-butylbenzo 18 crown 6 (DtBB18C6) onto poly(acrylamide-acrylic acid-acrylonitril)-N, N'-methylenediacrylamide (P(AM-AA-AN)-DAM). The removal of (134)Cs, (60)Co, (65)Zn , and ((152+154))Eu onto P(AM-AA-AN)-DAM/DtBB18C6 was investigated using a batch equilibrium technique with respect to the pH, contact time, and temperature. Kinetic models are used to determine the rate of sorption and to investigate the mechanism of sorption process. Five kinetics models, pseudo-first-order, pseudo-second-order, intra-particle diffusion, homogeneous particle diffusion (HPDM), and Elovich models, were used to investigate the sorption process. The obtained results of kinetic models predicted that, pseudo-second-order is applicable; the sorption is controlled by particle diffusion mechanism and the process is chemisorption. The obtained values of thermodynamics parameters, DeltaH degrees , DeltaS degrees , and DeltaG degrees indicated that the endothermic nature, increased randomness at the solid/solution interface and the spontaneous nature of the sorption processes. Copyright (c) 2009 Elsevier Ltd. All rights reserved.

Mercury adsorption in the Mississippi River deltaic plain freshwater marsh soil of Louisiana Gulf coastal wetlands.

PubMed

Park, Jong-Hwan; Wang, Jim J; Xiao, Ran; Pensky, Scott M; Kongchum, Manoch; DeLaune, Ronald D; Seo, Dong-Cheol

2018-03-01

Mercury adsorption characteristics of Mississippi River deltaic plain (MRDP) freshwater marsh soil in the Louisiana Gulf coast were evaluated under various conditions. Mercury adsorption was well described by pseudo-second order and Langmuir isotherm models with maximum adsorption capacity of 39.8 mg g -1 . Additional fitting of intraparticle model showed that mercury in the MRDP freshwater marsh soil was controlled by both external surface adsorption and intraparticle diffusion. The partition of adsorbed mercury (mg g -1 ) revealed that mercury was primarily adsorbed into organic-bond fraction (12.09) and soluble/exchangeable fraction (10.85), which accounted for 63.5% of the total adsorption, followed by manganese oxide-bound (7.50), easily mobilizable carbonate-bound (4.53), amorphous iron oxide-bound (0.55), crystalline Fe oxide-bound (0.41), and residual fraction (0.16). Mercury adsorption capacity was generally elevated along with increasing solution pH even though dominant species of mercury were non-ionic HgCl 2 , HgClOH and Hg(OH) 2  at between pH 3 and 9. In addition, increasing background NaCl concentration and the presence of humic acid decreased mercury adsorption, whereas the presence of phosphate, sulfate and nitrate enhanced mercury adsorption. Mercury adsorption in the MRDP freshwater marsh soil was reduced by the presence of Pb, Cu, Cd and Zn with Pb showing the greatest competitive adsorption. Overall the adsorption capacity of mercury in the MRDP freshwater marsh soil was found to be significantly influenced by potential environmental changes, and such factors should be considered in order to manage the risks associated with mercury in this MRDP wetland for responding to future climate change scenarios. Copyright © 2017 Elsevier Ltd. All rights reserved.

Electrochromatographic retention of peptides on strong cation-exchange stationary phases.

PubMed

Nischang, Ivo; Höltzel, Alexandra; Tallarek, Ulrich

2010-03-01

We analyze the systematic and substantial electrical field-dependence of electrochromatographic retention for four counterionic peptides ([Met5]enkephalin, oxytocin, [Arg8]vasopressin, and luteinizing hormone releasing hormone (LHRH) ) on a strong cation-exchange (SCX) stationary phase. Our experiments show that retention behavior in the studied system depends on the charge-selectivity of the stationary phase particles, the applied voltage, and the peptides' net charge. Retention factors of twice positively charged peptides ([Arg8]vasopressin and LHRH at pH 2.7) decrease with increasing applied voltage, whereas lower charged peptides (oxytocin and [Met5]enkephalin at pH 2.7, [Arg8]vasopressin and LHRH at pH 7.0) show a concomitant increase in their retention factors. The observed behavior is explained on the basis of electrical field-induced concentration polarization (CP) that develops around the SCX particles of the packing. The intraparticle concentration of charged species (buffer ions, peptides) increases with increasing applied voltage due to diffusive backflux from the enriched CP zone associated with each SCX particle. For twice charged and on the SCX phase strongly retained peptides the local increase in mobile phase ionic strength reduces the electrostatic interactions with the stationary phase, which explains the decrease of retention factors with increasing applied voltage and CP intensity. Lower charged and weaker retained peptides experience a much stronger relative intraparticle enrichment than the twice-charged peptides, which results in a net increase of retention factors with increasing applied voltage. The CP-related contribution to electrochromatographic retention of peptides on the SCX stationary phase is modulated by the applied voltage, the mobile phase ionic strength, and the peptides' net charge and could be used for selectivity tuning in difficult separations.

Group iterative methods for the solution of two-dimensional time-fractional diffusion equation

NASA Astrophysics Data System (ADS)

Balasim, Alla Tareq; Ali, Norhashidah Hj. Mohd.

2016-06-01

Variety of problems in science and engineering may be described by fractional partial differential equations (FPDE) in relation to space and/or time fractional derivatives. The difference between time fractional diffusion equations and standard diffusion equations lies primarily in the time derivative. Over the last few years, iterative schemes derived from the rotated finite difference approximation have been proven to work well in solving standard diffusion equations. However, its application on time fractional diffusion counterpart is still yet to be investigated. In this paper, we will present a preliminary study on the formulation and analysis of new explicit group iterative methods in solving a two-dimensional time fractional diffusion equation. These methods were derived from the standard and rotated Crank-Nicolson difference approximation formula. Several numerical experiments were conducted to show the efficiency of the developed schemes in terms of CPU time and iteration number. At the request of all authors of the paper an updated version of this article was published on 7 July 2016. The original version supplied to AIP Publishing contained an error in Table 1 and References 15 and 16 were incomplete. These errors have been corrected in the updated and republished article.

Phosphorous removal from aqueous solution can be enhanced through the calcination of lime sludge.

PubMed

Bal Krishna, K C; Niaz, Mohamed R; Sarker, Dipok C; Jansen, Troy

2017-09-15

Water treatment plants generate an enormous amount of the sludge which is normally treated as waste. In the recent past, many investigations have been focused on developing an economical adsorbent using water treatment sludge to remove phosphorous (P) from aqueous solutions. However, the great extents of the studies have been limited in the use of alum- and iron-based sludges. This study, therefore, investigated the P removal performance of the calcined lime sludge. Calcined lime sludge at 700 °C significantly enhanced the P removal efficiency whereas marginal improvement was noted when the sludge calcined at 400 °C was tested. With increase P removal efficiency, final pH values of the solution also significantly increased. P removal efficiency of the calcined sludge decreased with increasing the initial P concentrations. However, the removal efficiency could be improved by increasing the weight of the sludge. Further analysis demonstrated that P removal trend followed both pseudo-second order and diffusion-chemisorption kinetics signifying the P removal is potentially due to a multi-mechanistic reaction in which, the process is controlled by intra-particle diffusion followed by chemisorptions. Copyright © 2017 Elsevier Ltd. All rights reserved.

Sorption kinetics, isotherms, and mechanism of aniline aerofloat to agricultural soils with various physicochemical properties.

PubMed

Xiang, Lei; Xiao, Tao; Mo, Ce-Hui; Zhao, Hai-Ming; Li, Yan-Wen; Li, Hui; Cai, Quan-Ying; Zhou, Dong-Mei; Wong, Ming-Hung

2018-06-15

Aniline aerofloat (AAF), a high-toxic organic flotation reagent, is widely used in mineral processing industry. However, little information on its environmental fate is available. AAF sorption to four types of agricultural soils at low concentrations (1-10 mg/L) was investigated using batch experiments. AAF sorption kinetics involved both boundary layer diffusion and intraparticle diffusion, following pseudo-second-order kinetics with equilibrium time within 120 min. Both Langmuir and Freundlich models fitted well the AAF sorption with the former better. Sorption of AAF to soils was a spontaneous and favorable physical sorption that was controlled by ion bridge effect and hydrophobic interaction that was related to van der Waals force and π-π coordination based on FTIR analyses. AAF sorption was remarkably affected by soil constituents, positively correlating with the contents of organic matter and clay. The relatively higher logK oc values (3.53-4.66) of AAF at environmental concentrations (1-5 mg/L) imply that soils are serving as a sink of AAF from beneficiation wastewater, posing great potential risks to environment and human health. Copyright © 2018 Elsevier Inc. All rights reserved.

Tuning the Pore Geometry of Ordered Mesoporous Carbons for Enhanced Adsorption of Bisphenol-A

PubMed Central

Libbrecht, Wannes; Vandaele, Koen; De Buysser, Klaartje; Verberckmoes, An; Thybaut, Joris W.; Poelman, Hilde; De Clercq, Jeriffa; Van Der Voort, Pascal

2015-01-01

Mesoporous carbons were synthesized via both soft and hard template methods and compared to a commercial powder activated carbon (PAC) for the adsorption ability of bisphenol-A (BPA) from an aqueous solution. The commercial PAC had a BET-surface of 1027 m2/g with fine pores of 3 nm and less. The hard templated carbon (CMK-3) material had an even higher BET-surface of 1420 m2/g with an average pore size of 4 nm. The soft templated carbon (SMC) reached a BET-surface of 476 m2/g and a pore size of 7 nm. The maximum observed adsorption capacity (qmax) of CMK-3 was the highest with 474 mg/g, compared to 290 mg/g for PAC and 154 mg/g for SMC. The difference in adsorption capacities was attributed to the specific surface area and hydrophobicity of the adsorbent. The microporous PAC showed the slowest adsorption, while the ordered mesopores of SMC and CMK-3 enhanced the BPA diffusion into the adsorbent. This difference in adsorption kinetics is caused by the increase in pore diameter. However, CMK-3 with an open geometry consisting of interlinked nanorods allows for even faster intraparticle diffusion. PMID:28788023

Biosorption of As(III) and As(V) on the surface of TW/MnFe2O4 composite from wastewater: kinetics, mechanistic and thermodynamics

NASA Astrophysics Data System (ADS)

Podder, M. S.; Majumder, C. B.

2017-10-01

In the present study, TW/MnFe2O4 composite (MTW) was synthesized and estimated as an effective biosorbent for removing As (III) and As(V) from wastewater. Physicochemical analysis of composite was performed through SEM-EDX. 86.615 and 83.478% removal efficiency were obtained by composite dosage of 2 g/L at contact time 120 min at temperature 30 °C and pH 7.0 and 4.0 for As(III) and As(V), respectively. Kinetic results study showed that Brouers-Weron-Sotolongo and Ritchie second-order for As(III) and Brouers-Weron-Sotolongo model for As(V) were capable to describe an accurate explanation of adsorption kinetic. Applicability of mechanistic models in the current study exposed that the rate-controlling step in the biosorption of both As(III) and As(V) on the surface of composite was film diffusion rather than intraparticle diffusion. The estimated thermodynamic parameters Δ G 0, Δ H 0 and Δ S 0 revealed that the biosorption of both As(III) and As(V) on the composite was feasible, spontaneous and exothermic.

Application of granular activated carbon/MnFe2O4 composite immobilized on C. glutamicum MTCC 2745 to remove As(III) and As(V): Kinetic, mechanistic and thermodynamic studies

NASA Astrophysics Data System (ADS)

Podder, M. S.; Majumder, C. B.

2016-01-01

The main objective of the present study was to investigate the efficiency of Corynebacterium glutamicum MTCC 2745 immobilized on granular activated carbon/MnFe2O4 (GAC/MnFe2O4) composite to treat high concentration of arsenic bearing wastewater. Non-linear regression analysis was done for determining the best-fit kinetic model on the basis of three correlation coefficients and three error functions and also for predicting the parameters involved in kinetic models. The results showed that Fractal-like mixed 1,2 order model for As(III) and Brouser-Weron-Sototlongo as well as Fractal-like pseudo second order models for As(V) were proficient to provide realistic description of biosorption/bioaccumulation kinetic. Applicability of mechanistic models in the current study exhibited that the rate governing step in biosorption/bioaccumulation of both As(III) and As(V) was film diffusion rather than intraparticle diffusion. The evaluated thermodynamic parameters ΔG0, ΔH0 and ΔS0 revealed that biosorption/bioaccumulation of both As(III) and As(V) was feasible, spontaneous and exothermic under studied conditions.

Modeling, kinetic, and equilibrium characterization of paraquat adsorption onto polyurethane foam using the ion-pairing technique.

PubMed

Vinhal, Jonas O; Lage, Mateus R; Carneiro, José Walkimar M; Lima, Claudio F; Cassella, Ricardo J

2015-06-01

We studied the adsorption of paraquat onto polyurethane foam (PUF) when it was in a medium containing sodium dodecylsulfate (SDS). The adsorption efficiency was dependent on the concentration of SDS in solution, because the formation of an ion-associate between the cationic paraquat and the dodecylsulfate anion was found to be a fundamental step in the process. A computational study was carried out to identify the possible structure of the ion-associate in aqueous medium. The obtained data demonstrated that the structure is probably formed from four units of dodecylsulfate bonded to one paraquat moiety. The results showed that 94% of the paraquat present in 45 mL of a solution containing 3.90 × 10(-5) mol L(-1) could be retained by 300 mg of PUF, resulting in the removal of 2.20 mg of paraquat. The experimental data were reasonably adjusted to the Freundlich isotherm and to the pseudo-second-order kinetic model. Also, the application of Morris-Weber and Reichenberg models indicated that both film-diffusion and intraparticle-diffusion processes were active during the control of the adsorption kinetics. Copyright © 2015 Elsevier Ltd. All rights reserved.

The promise of a specially-designed graft copolymer of acrylic acid onto cellulose as selective sorbent for heavy metal ions.

PubMed

Essawy, Hisham A; Mohamed, Magdy F; Ammar, Nabila S; Ibrahim, Hanan S

2017-10-01

A specially-designed graft copolymer of acrylic acid onto in-situ formed cellulose-fulvate hybrid showed privileged tendency for uptake of Pb(II) during competitive removal from a mixture containing Cd(II) and Ni(II) within 5min at pH 5. This novel trend is attributed mainly to the crowded high content of coordinating centers within the designed graft copolymer along with the acquired superabsorbency. This provides an outstanding tool to separate some metal ions selectively from mixtures containing multiple ions on kinetic basis. Thus, the designed graft copolymer structure exhibited superior efficiency that reached ∼95% for sole removal of Pb(II). Kinetic modeling for Pb(II) individual removal showed excellent fitting with a pseudo second-order model. Intraparticle diffusion model on the other hand ensured governance of boundary layer effect over diffusion during the removal process due to the superabsorbency feature of the graft copolymer. The experimental findings were described with models such as Freundlich, Langmuir, and Dubinin-Radushkevich. The Langmuir and Freundlich models showed convenience with the adsorption isotherm of Pb(II) onto the developed graft copolymer. Copyright © 2017 Elsevier B.V. All rights reserved.

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

On the anisotropic advection-diffusion equation with time dependent coefficients

DOE PAGES

Hernandez-Coronado, Hector; Coronado, Manuel; Del-Castillo-Negrete, Diego B.

2017-02-01

The advection-diffusion equation with time dependent velocity and anisotropic time dependent diffusion tensor is examined in regard to its non-classical transport features and to the use of a non-orthogonal coordinate system. Although this equation appears in diverse physical problems, particularly in particle transport in stochastic velocity fields and in underground porous media, a detailed analysis of its solutions is lacking. In order to study the effects of the time-dependent coefficients and the anisotropic diffusion on transport, we solve analytically the equation for an initial Dirac delta pulse. Here, we discuss the solutions to three cases: one based on power-law correlationmore » functions where the pulse diffuses faster than the classical rate ~t, a second case specically designed to display slower rate of diffusion than the classical one, and a third case to describe hydrodynamic dispersion in porous media« less

General pulsed-field gradient signal attenuation expression based on a fractional integral modified-Bloch equation

NASA Astrophysics Data System (ADS)

Lin, Guoxing

2018-10-01

Anomalous diffusion has been investigated in many polymer and biological systems. The analysis of PFG anomalous diffusion relies on the ability to obtain the signal attenuation expression. However, the general analytical PFG signal attenuation expression based on the fractional derivative has not been previously reported. Additionally, the reported modified-Bloch equations for PFG anomalous diffusion in the literature yielded different results due to their different forms. Here, a new integral type modified-Bloch equation based on the fractional derivative for PFG anomalous diffusion is proposed, which is significantly different from the conventional differential type modified-Bloch equation. The merit of the integral type modified-Bloch equation is that the original properties of the contributions from linear or nonlinear processes remain unchanged at the instant of the combination. From the modified-Bloch equation, the general solutions are derived, which includes the finite gradient pulse width (FGPW) effect. The numerical evaluation of these PFG signal attenuation expressions can be obtained either by the Adomian decomposition, or a direct integration method that is fast and practicable. The theoretical results agree with the continuous-time random walk (CTRW) simulations performed in this paper. Additionally, the relaxation effect in PFG anomalous diffusion is found to be different from that in PFG normal diffusion. The new modified-Bloch equations and their solutions provide a fundamental tool to analyze PFG anomalous diffusion in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI).

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C072)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND SPEED AND EDDY DIFFUSIVITIES. (R825689C048)

EPA Science Inventory

Abstract

Three-dimensional analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities are derived in a systematic fashion. For homogeneous Neumann (total reflection), Dirichlet (total adsorpti...

Three-dimensional stochastic modeling of radiation belts in adiabatic invariant coordinates

NASA Astrophysics Data System (ADS)

Zheng, Liheng; Chan, Anthony A.; Albert, Jay M.; Elkington, Scot R.; Koller, Josef; Horne, Richard B.; Glauert, Sarah A.; Meredith, Nigel P.

2014-09-01

A 3-D model for solving the radiation belt diffusion equation in adiabatic invariant coordinates has been developed and tested. The model, named Radbelt Electron Model, obtains a probabilistic solution by solving a set of Itô stochastic differential equations that are mathematically equivalent to the diffusion equation. This method is capable of solving diffusion equations with a full 3-D diffusion tensor, including the radial-local cross diffusion components. The correct form of the boundary condition at equatorial pitch angle α0=90° is also derived. The model is applied to a simulation of the October 2002 storm event. At α0 near 90°, our results are quantitatively consistent with GPS observations of phase space density (PSD) increases, suggesting dominance of radial diffusion; at smaller α0, the observed PSD increases are overestimated by the model, possibly due to the α0-independent radial diffusion coefficients, or to insufficient electron loss in the model, or both. Statistical analysis of the stochastic processes provides further insights into the diffusion processes, showing distinctive electron source distributions with and without local acceleration.

A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation

NASA Astrophysics Data System (ADS)

Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon

2017-09-01

Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-01-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

NASA Astrophysics Data System (ADS)

Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue

2018-06-01

This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0. Furthermore, we prove the global existence and uniqueness of C^{α ,β }-solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1-space. The exponential convergence rate is also derived.

Diffusion phenomenon for linear dissipative wave equations in an exterior domain

NASA Astrophysics Data System (ADS)

Ikehata, Ryo

Under the general condition of the initial data, we will derive the crucial estimates which imply the diffusion phenomenon for the dissipative linear wave equations in an exterior domain. In order to derive the diffusion phenomenon for dissipative wave equations, the time integral method which was developed by Ikehata and Matsuyama (Sci. Math. Japon. 55 (2002) 33) plays an effective role.

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

A moving mesh finite difference method for equilibrium radiation diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

The equilibrium-diffusion limit for radiation hydrodynamics

DOE PAGES

Ferguson, J. M.; Morel, J. E.; Lowrie, R.

2017-07-27

The equilibrium-diffusion approximation (EDA) is used to describe certain radiation-hydrodynamic (RH) environments. When this is done the RH equations reduce to a simplified set of equations. The EDA can be derived by asymptotically analyzing the full set of RH equations in the equilibrium-diffusion limit. Here, we derive the EDA this way and show that it and the associated set of simplified equations are both first-order accurate with transport corrections occurring at second order. Having established the EDA’s first-order accuracy we then analyze the grey nonequilibrium-diffusion approximation and the grey Eddington approximation and show that they both preserve this first-order accuracy.more » Further, these approximations preserve the EDA’s first-order accuracy when made in either the comoving-frame (CMF) or the lab-frame (LF). And while analyzing the Eddington approximation, we found that the CMF and LF radiation-source equations are equivalent when neglecting O(β 2) terms and compared in the LF. Of course, the radiation pressures are not equivalent. It is expected that simplified physical models and numerical discretizations of the RH equations that do not preserve this first-order accuracy will not retain the correct equilibrium-diffusion solutions. As a practical example, we show that nonequilibrium-diffusion radiative-shock solutions devolve to equilibrium-diffusion solutions when the asymptotic parameter is small.« less

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

Removal of Cu(II) from leachate using natural zeolite as a landfill liner material.

PubMed

Turan, N Gamze; Ergun, Osman Nuri

2009-08-15

All hazardous waste disposal facilities require composite liner systems to act as a barrier against migration of contaminated leachate into the subsurface environment. Removal of copper(II) from leachate was studied using natural zeolite. A serial of laboratory systems on bentonite added natural zeolite was conducted and copper flotation waste was used as hazardous waste. The adsorption capacities and sorption efficiencies were determined. The sorption efficiencies increased with increasing natural zeolite ratio. The pseudo-first-order, the pseudo-second-order, Elovich and the intra-particle diffusion kinetic models were used to describe the kinetic data to estimate the rate constants. The second-order model best described adsorption kinetic data. The results indicated that natural zeolite showed excellent adsorptive characteristics for the removal of copper(II) from leachate and could be used as very good liner materials due to its high uptake capacity and the abundance in availability.

Experimental evidence of {alpha}-olefin readsorption in Fischer-Tropsch synthesis on ruthenium-supported ETS-10 titanium silicate catalysts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bianchi, C.L.; Ragaini, V.

1997-05-01

Fischer-Tropsch synthesis seems to develop the following two consecutive paths: a primary process that involves the formation of {alpha}-olefin products and a secondary process leading to the production of branched isomers and paraffins and requiring the readsorption of primary {alpha}-olefin products. It was already shown by Iglesia et al. that such readsorption steps are of fundamental importance for Ru catalysts and that they occur due to the slow diffusive removal of {alpha}-olefins when the molecular size increases, this resulting in a long intraparticle residence time. In the present paper {alpha}-olefins readsorption was enhanced by changing the metal distribution inside themore » pores of a titanium silicate (ETS-10), modified by ion exchange with alkali metal ions, used as a support for Ru-based catalysts. 24 refs., 5 figs., 3 tabs.« less

Application of activated carbon derived from scrap tires for adsorption of Rhodamine B.

PubMed

Li, Li; Liu, Shuangxi; Zhu, Tan

2010-01-01

Activated carbon derived from solid hazardous waste scrap tires was evaluated as a potential adsorbent for cationic dye removal. The adsorption process with respect to operating parameters was investigated to evaluate the adsorption characteristics of the activated pyrolytic tire char (APTC) for Rhodamine B (RhB). Systematic research including equilibrium, kinetics and thermodynamic studies was performed. The results showed that APTC was a potential adsorbent for RhB with a higher adsorption capacity than most adsorbents. Solution pH and temperature exert significant influence while ionic strength showed little effect on the adsorption process. The adsorption equilibrium data obey Langmuir isotherm and the kinetic data were well described by the pseudo second-order kinetic model. The adsorption process followed intra-particle diffusion model with more than one process affecting the adsorption process. Thermodynamic study confirmed that the adsorption was a physisorption process with spontaneous, endothermic and random characteristics.

Adsorption/electrosorption of catechol and resorcinol onto high area activated carbon cloth.

PubMed

Bayram, Edip; Hoda, Numan; Ayranci, Erol

2009-09-15

Removal of catechol and resorcinol from aqueous solutions by adsorption and electrosorption onto high area activated carbon cloth (ACC) was investigated. Kinetics of both adsorption and electrosorption were followed by in-situ UV-spectroscopic method and the data were treated according to pseudo-first-order, pseudo-second-order and intraparticle diffusion models. It was found that the adsorption and electrosorption of these compounds onto ACC follows pseudo-second-order model. pH changes during adsorption and electrosorption were followed and discussed with regard to the interaction between ACC and adsorbate molecules, utilizing the pH(pzc) value of ACC. An electrodesorption experiment was conducted to explore the possibility of regeneration of ACC. Adsorption isotherms were derived at 25 degrees C on the basis of batch analysis. The fits of experimental isotherm data to the well-known Freundlich, Langmuir and Tempkin models were examined.

Amination of activated carbon for enhancing phenol adsorption: Effect of nitrogen-containing functional groups

NASA Astrophysics Data System (ADS)

Yang, Guo; Chen, Honglin; Qin, Hangdao; Feng, Yujun

2014-02-01

To study the contribution of different nitrogen-containing functional groups to enhancement of phenol adsorption, the aminated activated carbons (AC) were characterized by N2 adsorption/desorption, XPS, Boehm titration, and pH drift method and tested for adsorption behaviors of phenol. Adsorption isotherm fitting revealed that the Langmuir model was preferred for the aminated ACs. The adsorption capacity per unit surface area (qm/SSABET) was linearly correlated with the amount of pyridinic and pyrrolic N, which suggested that these two functional groups played a critical role in phenol adsorption. The enhancement of adsorption capacity was attributed to the strengthened π-π dispersion between phenol and basal plane of AC by pyridinic, pyrrolic N. The adsorption kinetics was found to follow the pseudo-second-order kinetic model, and intraparticle diffusion was one of the rate-controlling steps in the adsorption process.

Adsorptive removal of patulin from aqueous solution using thiourea modified chitosan resin.

PubMed

Liu, Bingjie; Peng, Xiaoning; Chen, Wei; Li, Yang; Meng, Xianghong; Wang, Dongfeng; Yu, Guangli

2015-09-01

In the present paper, thiourea modified chitosan resin (TMCR) was firstly prepared through converting hydroxyl groups of chitosan resin into thiol groups, using glutaraldehyde as cross-linking agent and thiourea as modification agent. TMCR was characterized by FTIR, EDXS, SEM, XRD and AFM technologies. Batch adsorption experiments were performed to study the adsorption capacity of TMCR for patulin at different pH, temperature, contact time and patulin concentration. The result showed that TMCR was effective in removal of patulin from aqueous solution. The adsorption capacity of TMCR for patulin was 1.0 mg/g at pH 4.0, 25 °C for 24 h. Adsorption process could be well described by pseudo-first order model, Freundlich isotherm model and intraparticle diffusion model. It indicated that TMCR is expected to be a new material for patulin adsorption from aqueous solutions. Copyright © 2015 Elsevier B.V. All rights reserved.

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

DOE Office of Scientific and Technical Information (OSTI.GOV)

Oboh, I., E-mail: innocentoboh@uniuyo.edu.ng; Aluyor, E.; Audu, T.

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R{sup 2}), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used tomore » predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.« less

Conversion of agricultural residues into activated carbons for water purification: Application to arsenate removal.

PubMed

Torres-Perez, Jonatan; Gerente, Claire; Andres, Yves

2012-01-01

The conversion of two agricultural wastes, sugar beet pulp and peanut hulls, into sustainable activated carbons is presented and their potential application for the treatment of arsenate solution is investigated. A direct and physical activation is selected as well as a simple chemical treatment of the adsorbents. The material properties, such as BET surface areas, porous volumes, elemental analysis, ash contents and pH(PZC), of these alternative carbonaceous porous materials are determined and compared with a commercial granular activated carbon. An adsorption study based on experimental kinetic and equilibrium data is conducted in a batch reactor and completed by the use of different models (intraparticle diffusion, pseudo-second-order, Langmuir and Freundlich) and by isotherms carried out in natural waters. It is thus demonstrated that sugar beet pulp and peanut hulls are good precursors to obtain activated carbons for arsenate removal.

Kinetic modelling for zinc (II) ions biosorption onto Luffa cylindrica

NASA Astrophysics Data System (ADS)

Oboh, I.; Aluyor, E.; Audu, T.

2015-03-01

The biosorption of Zinc (II) ions onto a biomaterial - Luffa cylindrica has been studied. This biomaterial was characterized by elemental analysis, surface area, pore size distribution, scanning electron microscopy, and the biomaterial before and after sorption, was characterized by Fourier Transform Infra Red (FTIR) spectrometer. The kinetic nonlinear models fitted were Pseudo-first order, Pseudo-second order and Intra-particle diffusion. A comparison of non-linear regression method in selecting the kinetic model was made. Four error functions, namely coefficient of determination (R2), hybrid fractional error function (HYBRID), average relative error (ARE), and sum of the errors squared (ERRSQ), were used to predict the parameters of the kinetic models. The strength of this study is that a biomaterial with wide distribution particularly in the tropical world and which occurs as waste material could be put into effective utilization as a biosorbent to address a crucial environmental problem.

A Hydrodynamic Theory for Spatially Inhomogeneous Semiconductor Lasers: Microscopic Approach

NASA Technical Reports Server (NTRS)

Li, Jianzhong; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2001-01-01

Starting from the microscopic semiconductor Bloch equations (SBEs) including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole (e-h) and carrier-LO (c-LO) phonon scatterings are directly used to derive the momentum and energy relaxation rates. These rates expressed as functions of temperatures and densities lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma (EHP) to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-h scattering dominates over c-LO phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-h scattering, even though the diffusion coefficients of individual components depend sensitively on the e-h scattering rates. Our discussions lead to new perspectives into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization which in turn couples to the laser field.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

The precise time-dependent solution of the Fokker–Planck equation with anomalous diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guo, Ran; Du, Jiulin, E-mail: jiulindu@aliyun.com

2015-08-15

We study the time behavior of the Fokker–Planck equation in Zwanzig’s rule (the backward-Ito’s rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation–dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker–Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution. - Highlights: • The precise time-dependent solution of the Fokker–Planck equation with anomalousmore » diffusion is found. • The anomalous diffusion satisfies a generalized fluctuation–dissipation relation. • At long time the time-dependent solution approaches to a power-law distribution in nonextensive statistics. • Numerically we have demonstrated the accuracy and validity of the time-dependent solution.« less

Projecting diffusion along the normal bundle of a plane curve

DOE Office of Scientific and Technical Information (OSTI.GOV)

Valero-Valdés, Carlos; Herrera-Guzmán, Rafael

2014-05-15

The purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized Fick-Jacob's equation obtained by projecting the two-dimensional diffusion equation along the normal directions of an arbitrary curve on the plane.

Kinetic study on removal of heavy metal ions from aqueous solution by using soil.

PubMed

Lim, Soh-Fong; Lee, Agnes Yung Weng

2015-07-01

In the present study, the feasibility of soil used as a low-cost adsorbent for the removal of Cu(2+), Zn(2+), and Pb(2+) ions from aqueous solution was investigated. The kinetics for adsorption of the heavy metal ions from aqueous solution by soil was examined under batch mode. The influence of the contact time and initial concentration for the adsorption process at pH of 4.5, under a constant room temperature of 25 ± 1 °C were studied. The adsorption capacity of the three heavy metal ions from aqueous solution was decreased in order of Pb(2+) > Cu(2+) > Zn(2+). The soil was characterized by Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopic-energy dispersive X-ray (SEM-EDX), and Brunauer, Emmett, and Teller (BET) surface area analyzer. From the FTIR analysis, the experimental data was corresponded to the peak changes of the spectra obtained before and after adsorption process. Studies on SEM-EDX showed distinct adsorption of the heavy metal ions and the mineral composition in the study areas were determined to be silica (SiO2), alumina (Al2O3), and iron(III) oxide (FeO3). A distinct decrease of the specific surface area and total pore volumes of the soil after adsorption was found from the BET analysis. The experimental results obtained were analyzed using four adsorption kinetic models, namely pseudo-first-order, pseudo-second-order, Elovich, and intraparticle diffusion. Evaluating the linear correlation coefficients, the kinetic studies showed that pseudo-second-order equation described the data appropriable than others. It was concluded that soil can be used as an effective adsorbent for removing Cu(2+), Zn(2+), and Pb(2+) ions from aqueous solution.

NUMERICAL ANALYSES FOR TREATING DIFFUSION IN SINGLE-, TWO-, AND THREE-PHASE BINARY ALLOY SYSTEMS

NASA Technical Reports Server (NTRS)

Tenney, D. R.

1994-01-01

This package consists of a series of three computer programs for treating one-dimensional transient diffusion problems in single and multiple phase binary alloy systems. An accurate understanding of the diffusion process is important in the development and production of binary alloys. Previous solutions of the diffusion equations were highly restricted in their scope and application. The finite-difference solutions developed for this package are applicable for planar, cylindrical, and spherical geometries with any diffusion-zone size and any continuous variation of the diffusion coefficient with concentration. Special techniques were included to account for differences in modal volumes, initiation and growth of an intermediate phase, disappearance of a phase, and the presence of an initial composition profile in the specimen. In each analysis, an effort was made to achieve good accuracy while minimizing computation time. The solutions to the diffusion equations for single-, two-, and threephase binary alloy systems are numerically calculated by the three programs NAD1, NAD2, and NAD3. NAD1 treats the diffusion between pure metals which belong to a single-phase system. Diffusion in this system is described by a one-dimensional Fick's second law and will result in a continuous composition variation. For computational purposes, Fick's second law is expressed as an explicit second-order finite difference equation. Finite difference calculations are made by choosing the grid spacing small enough to give convergent solutions of acceptable accuracy. NAD2 treats diffusion between pure metals which form a two-phase system. Diffusion in the twophase system is described by two partial differential equations (a Fick's second law for each phase) and an interface-flux-balance equation which describes the location of the interface. Actual interface motion is obtained by a mass conservation procedure. To account for changes in the thicknesses of the two phases as diffusion progresses, a variable grid technique developed by Murray and Landis is employed. These equations are expressed in finite difference form and solved numerically. Program NAD3 treats diffusion between pure metals which form a two-phase system with an intermediate third phase. Diffusion in the three-phase system is described by three partial differential expressions of Fick's second law and two interface-flux-balance equations. As with the two-phase case, a variable grid finite difference is used to numerically solve the diffusion equations. Computation time is minimized without sacrificing solution accuracy by treating the three-phase problem as a two-phase problem when the thickness of the intermediate phase is less than a preset value. Comparisons between these programs and other solutions have shown excellent agreement. The programs are written in FORTRAN IV for batch execution on the CDC 6600 with a central memory requirement of approximately 51K (octal) 60 bit words.

Fractional diffusion on bounded domains

DOE PAGES

Defterli, Ozlem; D'Elia, Marta; Du, Qiang; ...

2015-03-13

We found that the mathematically correct specification of a fractional differential equation on a bounded domain requires specification of appropriate boundary conditions, or their fractional analogue. In this paper we discuss the application of nonlocal diffusion theory to specify well-posed fractional diffusion equations on bounded domains.

Preparation of nanomaterials for the ultrasound-enhanced removal of Pb2+ ions and malachite green dye: Chemometric optimization and modeling.

PubMed

Dil, Ebrahim Alipanahpour; Ghaedi, Mehrorang; Asfaram, Arash; Hajati, Shaaker; Mehrabi, Fatemeh; Goudarzi, Alireza

2017-01-01

Copper oxide nanoparticle-loaded activated carbon (CuO-NP-AC) was synthesized and characterized using different techniques such as FE-SEM, XRD and FT-IR. It was successfully applied for the ultrasound-assisted simultaneous removal of Pb 2+ ions and malachite green (MG) dye in binary system from aqueous solution. The effect of important parameters was modeled and optimized by artificial neural network (ANN) and response surface methodology (RSM). Maximum simultaneous removal percentages (>99.0%) were found at 25mgL -1 , 20mgL -1 , 0.02g, 5min and 6.0 corresponding to initial Pb 2+ concentration, initial MG concentration, CuO-NP-AC amount, ultrasonication time and pH, respectively. The precision of the equation obtained by RSM was confirmed by the analysis of variance and calculation of correlation coefficient relating the predicted and the experimental values of ultrasound-assisted simultaneous removal of the analytes. A good agreement between experimental and predicted values was observed. A feed-forward neural network with a topology optimized by response surface methodology was successfully applied for the prediction of ultrasound-assisted simultaneous removal of Pb 2+ ions and MG dye in binary system by CuO-NPs-AC. The number of hidden neurons, MSE, R 2 , number of epochs and error histogram were chosen for ANN modeling. Then, Langmuir, Freundlich, Temkin and D-R isothermal models were applied for fitting the experimental data. It was found that the Langmuir model well describes the isotherm data with a maximum adsorption capacity of 98.328 and 87.719mgg -1 for Pb 2+ and MG, respectively. Kinetic studies at optimum condition showed that maximum Pb 2+ and MG adsorption is achieved within 5min of the start of most experiments. The combination of pseudo-second-order rate equation and intraparticle diffusion model was applicable to explain the experimental data of ultrasound-assisted simultaneous removal of Pb 2+ and MG at optimum condition obtained from RSM. Copyright © 2016 Elsevier B.V. All rights reserved.

Mathematics of thermal diffusion in an exponential temperature field

NASA Astrophysics Data System (ADS)

Zhang, Yaqi; Bai, Wenyu; Diebold, Gerald J.

2018-04-01

The Ludwig-Soret effect, also known as thermal diffusion, refers to the separation of gas, liquid, or solid mixtures in a temperature gradient. The motion of the components of the mixture is governed by a nonlinear, partial differential equation for the density fractions. Here solutions to the nonlinear differential equation for a binary mixture are discussed for an externally imposed, exponential temperature field. The equation of motion for the separation without the effects of mass diffusion is reduced to a Hamiltonian pair from which spatial distributions of the components of the mixture are found. Analytical calculations with boundary effects included show shock formation. The results of numerical calculations of the equation of motion that include both thermal and mass diffusion are given.

Double diffusivity model under stochastic forcing

NASA Astrophysics Data System (ADS)

Chattopadhyay, Amit K.; Aifantis, Elias C.

2017-05-01

The "double diffusivity" model was proposed in the late 1970s, and reworked in the early 1980s, as a continuum counterpart to existing discrete models of diffusion corresponding to high diffusivity paths, such as grain boundaries and dislocation lines. It was later rejuvenated in the 1990s to interpret experimental results on diffusion in polycrystalline and nanocrystalline specimens where grain boundaries and triple grain boundary junctions act as high diffusivity paths. Technically, the model pans out as a system of coupled Fick-type diffusion equations to represent "regular" and "high" diffusivity paths with "source terms" accounting for the mass exchange between the two paths. The model remit was extended by analogy to describe flow in porous media with double porosity, as well as to model heat conduction in media with two nonequilibrium local temperature baths, e.g., ion and electron baths. Uncoupling of the two partial differential equations leads to a higher-ordered diffusion equation, solutions of which could be obtained in terms of classical diffusion equation solutions. Similar equations could also be derived within an "internal length" gradient (ILG) mechanics formulation applied to diffusion problems, i.e., by introducing nonlocal effects, together with inertia and viscosity, in a mechanics based formulation of diffusion theory. While being remarkably successful in studies related to various aspects of transport in inhomogeneous media with deterministic microstructures and nanostructures, its implications in the presence of stochasticity have not yet been considered. This issue becomes particularly important in the case of diffusion in nanopolycrystals whose deterministic ILG-based theoretical calculations predict a relaxation time that is only about one-tenth of the actual experimentally verified time scale. This article provides the "missing link" in this estimation by adding a vital element in the ILG structure, that of stochasticity, that takes into account all boundary layer fluctuations. Our stochastic-ILG diffusion calculation confirms rapprochement between theory and experiment, thereby benchmarking a new generation of gradient-based continuum models that conform closer to real-life fluctuating environments.

Iron-impregnated granular activated carbon for arsenic removal from drinking water

NASA Astrophysics Data System (ADS)

Chang, Qigang

A new multi-step iron impregnation method was developed in this study to impregnate GAC with a high amount of iron that possesses desired characteristics: stable, even distribution, and high arsenic adsorption capacity. Research was carried out to investigate the impact of the amount of impregnated iron on arsenic adsorption properties: capacity, affinity, and kinetics. Fe-GACs were characterized in terms of the amount, stability, distribution, morphology, and species of impregnated iron. It was found that a high amount of iron was stably impregnated in GAC. Scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) analysis demonstrated that the impregnated iron was evenly distributed on the internal surface of GAC. Impregnated iron formed nano-size particles and existed in both crystalline (akaganeite) and amorphous iron. Arsenic adsorption tests were conducted using Fe-GACs with iron content of 1.64--28.90% in a low arsenic concentration that is typical for drinking water treatment. The amount of impregnated iron affects arsenic maximum adsorption capacity (qm) but has little impact on the Langmuir constant h (the affinity of adsorbent for adsorbate). The qm for both As(V) and As(III) adsorptions increased significantly with increase of the amount of impregnated iron up to 13.59%. Further increase of iron amounts caused a gradual decrease of qm for As(V). BET analysis indicated impregnated iron possesses the highest surface area at iron content of 13.59%. A new second-order kinetic model was developed to investigate the impact of the amounts of impregnated iron on arsenic adsorption kinetics. With iron content increased from 1.64% to 28.90%, the intrinsic adsorption rate constants reduced from 4.6x10-2 1/hr to 1.18x10 -3 1/hr, which indicates that impregnated iron slows arsenic intraparticle diffusion rate in Fe-GAC. The decreased arsenic intraparticle diffusion rate was most likely caused by reduced pore size of Fe-GACs. Column tests were conducted to investigate the performance of Fe-GACs in real implementations using groundwater taken from a former superfund site in North Dakota. Fe-GACs can remove arsenic below 10 microg/L and the performance of Fe-GACs was significantly enhanced with increasing empty bed contact time.

Rarefied gas flows through a curved channel: Application of a diffusion-type equation

NASA Astrophysics Data System (ADS)

Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki

2010-11-01

Rarefied gas flows through a curved two-dimensional channel, caused by a pressure or a temperature gradient, are investigated numerically by using a macroscopic equation of convection-diffusion type. The equation, which was derived systematically from the Bhatnagar-Gross-Krook model of the Boltzmann equation and diffuse-reflection boundary condition in a previous paper [K. Aoki et al., "A diffusion model for rarefied flows in curved channels," Multiscale Model. Simul. 6, 1281 (2008)], is valid irrespective of the degree of gas rarefaction when the channel width is much shorter than the scale of variations of physical quantities and curvature along the channel. Attention is also paid to a variant of the Knudsen compressor that can produce a pressure raise by the effect of the change of channel curvature and periodic temperature distributions without any help of moving parts. In the process of analysis, the macroscopic equation is (partially) extended to the case of the ellipsoidal-statistical model of the Boltzmann equation.

Numerical applications of the advective-diffusive codes for the inner magnetosphere

NASA Astrophysics Data System (ADS)

Aseev, N. A.; Shprits, Y. Y.; Drozdov, A. Y.; Kellerman, A. C.

2016-11-01

In this study we present analytical solutions for convection and diffusion equations. We gather here the analytical solutions for the one-dimensional convection equation, the two-dimensional convection problem, and the one- and two-dimensional diffusion equations. Using obtained analytical solutions, we test the four-dimensional Versatile Electron Radiation Belt code (the VERB-4D code), which solves the modified Fokker-Planck equation with additional convection terms. The ninth-order upwind numerical scheme for the one-dimensional convection equation shows much more accurate results than the results obtained with the third-order scheme. The universal limiter eliminates unphysical oscillations generated by high-order linear upwind schemes. Decrease in the space step leads to convergence of a numerical solution of the two-dimensional diffusion equation with mixed terms to the analytical solution. We compare the results of the third- and ninth-order schemes applied to magnetospheric convection modeling. The results show significant differences in electron fluxes near geostationary orbit when different numerical schemes are used.

Fractional-calculus diffusion equation

PubMed Central

2010-01-01

Background Sequel to the work on the quantization of nonconservative systems using fractional calculus and quantization of a system with Brownian motion, which aims to consider the dissipation effects in quantum-mechanical description of microscale systems. Results The canonical quantization of a system represented classically by one-dimensional Fick's law, and the diffusion equation is carried out according to the Dirac method. A suitable Lagrangian, and Hamiltonian, describing the diffusive system, are constructed and the Hamiltonian is transformed to Schrodinger's equation which is solved. An application regarding implementation of the developed mathematical method to the analysis of diffusion, osmosis, which is a biological application of the diffusion process, is carried out. Schrödinger's equation is solved. Conclusions The plot of the probability function represents clearly the dissipative and drift forces and hence the osmosis, which agrees totally with the macro-scale view, or the classical-version osmosis. PMID:20492677

An asymptotic induced numerical method for the convection-diffusion-reaction equation

NASA Technical Reports Server (NTRS)

Scroggs, Jeffrey S.; Sorensen, Danny C.

1988-01-01

A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method.

A new Eulerian model for viscous and heat conducting compressible flows

NASA Astrophysics Data System (ADS)

Svärd, Magnus

2018-09-01

In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the Lagrangian derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely Eulerian framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.

Analytical solution of the nonlinear diffusion equation

NASA Astrophysics Data System (ADS)

Shanker Dubey, Ravi; Goswami, Pranay

2018-05-01

In the present paper, we derive the solution of the nonlinear fractional partial differential equations using an efficient approach based on the q -homotopy analysis transform method ( q -HATM). The fractional diffusion equations derivatives are considered in Caputo sense. The derived results are graphically demonstrated as well.

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

A flexible nonlinear diffusion acceleration method for the S N transport equations discretized with discontinuous finite elements

DOE PAGES

Schunert, Sebastian; Wang, Yaqi; Gleicher, Frederick; ...

2017-02-21

This paper presents a flexible nonlinear diffusion acceleration (NDA) method that discretizes both the S N transport equation and the diffusion equation using the discontinuous finite element method (DFEM). The method is flexible in that the diffusion equation can be discretized on a coarser mesh with the only restriction that it is nested within the transport mesh and the FEM shape function orders of the two equations can be different. The consistency of the transport and diffusion solutions at convergence is defined by using a projection operator mapping the transport into the diffusion FEM space. The diffusion weak form ismore » based on the modified incomplete interior penalty (MIP) diffusion DFEM discretization that is extended by volumetric drift, interior face, and boundary closure terms. In contrast to commonly used coarse mesh finite difference (CMFD) methods, the presented NDA method uses a full FEM discretized diffusion equation for acceleration. Suitable projection and prolongation operators arise naturally from the FEM framework. Via Fourier analysis and numerical experiments for a one-group, fixed source problem the following properties of the NDA method are established for structured quadrilateral meshes: (1) the presented method is unconditionally stable and effective in the presence of mild material heterogeneities if the same mesh and identical shape functions either of the bilinear or biquadratic type are used, (2) the NDA method remains unconditionally stable in the presence of strong heterogeneities, (3) the NDA method with bilinear elements extends the range of effectiveness and stability by a factor of two when compared to CMFD if a coarser diffusion mesh is selected. In addition, the method is tested for solving the C5G7 multigroup, eigenvalue problem using coarse and fine mesh acceleration. Finally, while NDA does not offer an advantage over CMFD for fine mesh acceleration, it reduces the iteration count required for convergence by almost a factor of two in the case of coarse mesh acceleration.« less

The effective boundary conditions and their lifespan of the logistic diffusion equation on a coated body

NASA Astrophysics Data System (ADS)

Li, Huicong; Wang, Xuefeng; Wu, Yanxia

2014-11-01

We consider the logistic diffusion equation on a bounded domain, which has two components with a thin coating surrounding a body. The diffusion tensor is isotropic on the body, and anisotropic on the coating. The size of the diffusion tensor on these components may be very different; within the coating, the diffusion rates in the normal and tangent directions may be in different scales. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the diffusion equation on the boundary of the body. We also prove that the lifespan of each EBC, which measures how long the EBC remains effective, is infinite. The EBCs enable us to see clearly the effect of the coating and ease the difficult task of solving the PDE in a thin region with a small diffusion tensor. The motivation of the mathematics includes a nature reserve surrounded by a buffer zone.

Worst case prediction of additives migration from polystyrene for food safety purposes: a model update.

PubMed

Martínez-López, Brais; Gontard, Nathalie; Peyron, Stéphane

2018-03-01

A reliable prediction of migration levels of plastic additives into food requires a robust estimation of diffusivity. Predictive modelling of diffusivity as recommended by the EU commission is carried out using a semi-empirical equation that relies on two polymer-dependent parameters. These parameters were determined for the polymers most used by packaging industry (LLDPE, HDPE, PP, PET, PS, HIPS) from the diffusivity data available at that time. In the specific case of general purpose polystyrene, the diffusivity data published since then shows that the use of the equation with the original parameters results in systematic underestimation of diffusivity. The goal of this study was therefore, to propose an update of the aforementioned parameters for PS on the basis of up to date diffusivity data, so the equation can be used for a reasoned overestimation of diffusivity.

Modeling Morphogenesis with Reaction-Diffusion Equations Using Galerkin Spectral Methods

DTIC Science & Technology

2002-05-06

reaction- diffusion equation is a difficult problem in analysis that will not be addressed here. Errors will also arise from numerically approx solutions to...the ODEs. When comparing the approximate solution to actual reaction- diffusion systems found in nature, we must also take into account errors that...

Exact Solutions of Coupled Multispecies Linear Reaction–Diffusion Equations on a Uniformly Growing Domain

PubMed Central

Simpson, Matthew J.; Sharp, Jesse A.; Morrow, Liam C.; Baker, Ruth E.

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction–diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction–diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially–confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially–confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit. PMID:26407013

Exact Solutions of Coupled Multispecies Linear Reaction-Diffusion Equations on a Uniformly Growing Domain.

PubMed

Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E

2015-01-01

Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.

An accurate computational method for the diffusion regime verification

NASA Astrophysics Data System (ADS)

Zhokh, Alexey A.; Strizhak, Peter E.

2018-04-01

The diffusion regime (sub-diffusive, standard, or super-diffusive) is defined by the order of the derivative in the corresponding transport equation. We develop an accurate computational method for the direct estimation of the diffusion regime. The method is based on the derivative order estimation using the asymptotic analytic solutions of the diffusion equation with the integer order and the time-fractional derivatives. The robustness and the computational cheapness of the proposed method are verified using the experimental methane and methyl alcohol transport kinetics through the catalyst pellet.

Continuous biosorption of Pb/Cu and Pb/Cd in fixed-bed column using algae Gelidium and granulated agar extraction algal waste.

PubMed

Vilar, Vítor J P; Loureiro, José M; Botelho, Cidália M S; Boaventura, Rui A R

2008-06-15

Continuous metal ions biosorption from Pb/Cu and Pb/Cd solutions onto seaweed Gelidium sesquipedale and a composite material prepared from an industrial algal waste was performed in a packed bed column. A binary Langmuir equation describes well the equilibrium data and indicates a good adsorption capacity. In the sorption process, Cd and Cu break through the column faster than Pb due to its lower affinity for the biosorbent. An overshoot in the outlet Cd concentration was observed and explained by competitive adsorption between Pb and Cd, whereby the higher Pb affinity for the biosorbent displaces bound Cd ions. A small overshoot happens for Cu adsorption in the presence of Pb ions. Desorption using 0.1 M HNO3 as eluant, was 100% effective. A mass transfer model for the adsorption and desorption processes, considering an external and intraparticle film resistance, adequately simulates the column performance. A binary Langmuir equation was used to describe equilibrium for the saturation process and a mass action law for the desorption process. Elution process is defined as an ion exchange mechanism, between protons and metal ions.

Adsorption of pharmaceuticals onto trimethylsilylated mesoporous SBA-15.

PubMed

Bui, Tung Xuan; Pham, Viet Hung; Le, Son Thanh; Choi, Heechul

2013-06-15

The adsorption of a complex mixture of 12 selected pharmaceuticals to trimethylsilylated mesoporous SBA-15 (TMS-SBA-15) has been investigated by batch adsorption experiments. The adsorption of pharmaceuticals to TMS-SBA-15 was highly dependent on the solution pH and pharmaceutical properties (i.e., hydrophobicity (logKow) and acidity (pKa)). Good log-log linear relationships between the adsorption (Kd) and pH-dependent octanol-water coefficients (Kow(pH)) were then established among the neutral, anionic, and cationic compounds, suggesting hydrophobic interaction as a primary driving force in the adsorption. In addition, the neutral species of each compound accounted for a major contribution to the overall compound adsorption onto TMS-SBA-15. The adsorption kinetics of pharmaceuticals was evaluated by the nonlinear first-order and pseudo-second-order models. The first-order model gave a better fit for five pharmaceuticals with lower adsorption capacity, whereas the pseudo-second-order model fitted better for seven pharmaceuticals having higher adsorption capacity. In the same group of properties, pharmaceuticals having higher adsorption capacity exhibited faster adsorption rates. The rate-limiting steps for adsorption of pharmaceuticals onto TMS-SBA-15 are boundary layer diffusion and intraparticle diffusion including diffusion in mesopores and micropores. In addition, the adsorption of pharmaceuticals to TMS-SBA-15 was not influenced by the change of initial pharmaceutical concentration (10-100μgL(-1)) and the presence of natural organic matter. Copyright © 2013 Elsevier B.V. All rights reserved.

Control of reaction-diffusion equations on time-evolving manifolds.

PubMed

Rossi, Francesco; Duteil, Nastassia Pouradier; Yakoby, Nir; Piccoli, Benedetto

2016-12-01

Among the main actors of organism development there are morphogens, which are signaling molecules diffusing in the developing organism and acting on cells to produce local responses. Growth is thus determined by the distribution of such signal. Meanwhile, the diffusion of the signal is itself affected by the changes in shape and size of the organism. In other words, there is a complete coupling between the diffusion of the signal and the change of the shapes. In this paper, we introduce a mathematical model to investigate such coupling. The shape is given by a manifold, that varies in time as the result of a deformation given by a transport equation. The signal is represented by a density, diffusing on the manifold via a diffusion equation. We show the non-commutativity of the transport and diffusion evolution by introducing a new concept of Lie bracket between the diffusion and the transport operator. We also provide numerical simulations showing this phenomenon.

Tunable intraparticle frameworks for creating complex heterostructured nanoparticle libraries

NASA Astrophysics Data System (ADS)

Fenton, Julie L.; Steimle, Benjamin C.; Schaak, Raymond E.

2018-05-01

Complex heterostructured nanoparticles with precisely defined materials and interfaces are important for many applications. However, rationally incorporating such features into nanoparticles with rigorous morphology control remains a synthetic bottleneck. We define a modular divergent synthesis strategy that progressively transforms simple nanoparticle synthons into increasingly sophisticated products. We introduce a series of tunable interfaces into zero-, one-, and two-dimensional copper sulfide nanoparticles using cation exchange reactions. Subsequent manipulation of these intraparticle frameworks yielded a library of 47 distinct heterostructured metal sulfide derivatives, including particles that contain asymmetric, patchy, porous, and sculpted nanoarchitectures. This generalizable mix-and-match strategy provides predictable retrosynthetic pathways to complex nanoparticle features that are otherwise inaccessible.

Fractional Number Operator and Associated Fractional Diffusion Equations

NASA Astrophysics Data System (ADS)

Rguigui, Hafedh

2018-03-01

In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator.

Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities

PubMed Central

Vázquez, J. L.

2010-01-01

The goal of this paper is to state the optimal decay rate for solutions of the nonlinear fast diffusion equation and, in self-similar variables, the optimal convergence rates to Barenblatt self-similar profiles and their generalizations. It relies on the identification of the optimal constants in some related Hardy–Poincaré inequalities and concludes a long series of papers devoted to generalized entropies, functional inequalities, and rates for nonlinear diffusion equations. PMID:20823259

Note on coefficient matrices from stochastic Galerkin methods for random diffusion equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Tao, E-mail: tzhou@lsec.cc.ac.c; Tang Tao, E-mail: ttang@hkbu.edu.h

2010-11-01

In a recent work by Xiu and Shen [D. Xiu, J. Shen, Efficient stochastic Galerkin methods for random diffusion equations, J. Comput. Phys. 228 (2009) 266-281], the Galerkin methods are used to solve stochastic diffusion equations in random media, where some properties for the coefficient matrix of the resulting system are provided. They also posed an open question on the properties of the coefficient matrix. In this work, we will provide some results related to the open question.

General solution of a fractional Parker diffusion-convection equation describing the superdiffusive transport of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, Ashraf M.; Fichtner, Horst; Elhanbaly, A.; Schlickeiser, Reinhard

2018-06-01

Anomalous diffusion models of energetic particles in space plasmas are developed by introducing the fractional Parker diffusion-convection equation. Analytical solution of the space-time fractional equation is obtained by use of the Caputo and Riesz-Feller fractional derivatives with the Laplace-Fourier transforms. The solution is given in terms of the Fox H-function. Profiles of particle densities are illustrated for different values of the space fractional order and the so-called skewness parameter.

Stress, deformation and diffusion interactions in solids - A simulation study

NASA Astrophysics Data System (ADS)

Fischer, F. D.; Svoboda, J.

2015-05-01

Equations of diffusion treated in the frame of Manning's concept, are completed by equations for generation/annihilation of vacancies at non-ideal sources and sinks, by conservation laws, by equations for generation of an eigenstrain state and by a strain-stress analysis. The stress-deformation-diffusion interactions are demonstrated on the evolution of a diffusion couple consisting of two thin layers of different chemical composition forming a free-standing plate without external loading. The equations are solved for different material parameters represented by the values of diffusion coefficients of individual components and by the intensity of sources and sinks for vacancies. The results of simulations indicate that for low intensity of sources and sinks for vacancies a significant eigenstress state can develop and the interdiffusion process is slowed down. For high intensity of sources and sinks for vacancies a significant eigenstrain state can develop and the eigenstress state quickly relaxes. If the difference in the diffusion coefficients of individual components is high, then the intensity of sources and sinks for vacancies influences the interdiffusion process considerably. For such systems their description only by diffusion coefficients is insufficient and must be completed by a microstructure characterization.

A double medium model for diffusion in fluid-bearing rock

NASA Astrophysics Data System (ADS)

Wang, H. F.

1993-09-01

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.

Diffusion in the special theory of relativity.

PubMed

Herrmann, Joachim

2009-11-01

The Markovian diffusion theory is generalized within the framework of the special theory of relativity. Since the velocity space in relativity is a hyperboloid, the mathematical stochastic calculus on Riemanian manifolds can be applied but adopted here to the velocity space. A generalized Langevin equation in the fiber space of position, velocity, and orthonormal velocity frames is defined from which the generalized relativistic Kramers equation in the phase space in external force fields is derived. The obtained diffusion equation is invariant under Lorentz transformations and its stationary solution is given by the Jüttner distribution. Besides, a nonstationary analytical solution is derived for the example of force-free relativistic diffusion.

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

NASA Astrophysics Data System (ADS)

Abd-El-Malek, Mina B.; Kassem, Magda M.; Meky, Mohammed L. M.

2002-03-01

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.

Ionic conduction and self-diffusion near infinitesimal concentration in lithium salt-organic solvent electrolytes

NASA Astrophysics Data System (ADS)

Aihara, Yuichi; Sugimoto, Kyoko; Price, William S.; Hayamizu, Kikuko

2000-08-01

The Debye-Hückel-Onsager and Nernst-Einstein equations, which are based on two different conceptual approaches, constitute the most widely used equations for relating ionic conduction to ionic mobility. However, both of these classical (simple) equations are predictive of ionic conductivity only at very low salt concentrations. In the present work the ionic conductivity of four organic solvent-lithium salt-based electrolytes were measured. These experimental conductivity values were then contrasted with theoretical values calculated using the translational diffusion (also known as self-diffusion or intradiffusion) coefficients of all of the species present obtained using pulsed-gradient spin-echo (1H, 19F and 7Li) nuclear magnetic resonance self-diffusion measurements. The experimental results verified the applicability of both theoretical approaches at very low salt concentrations for these particular systems as well as helping to clarify the reasons for the divergence between theory and experiment. In particular, it was found that the correspondence between the Debye-Hückel-Onsager equation and experimental values could be improved by using the measured solvent self-diffusion values to correct for salt-induced changes in the solution viscosity. The concentration dependence of the self-diffusion coefficients is discussed in terms of the Jones-Dole equation.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM.

PubMed

Singh, Brajesh K; Srivastava, Vineet K

2015-04-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.

Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

PubMed Central

Singh, Brajesh K.; Srivastava, Vineet K.

2015-01-01

The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations. PMID:26064639

Obstructions to Existence in Fast-Diffusion Equations

NASA Astrophysics Data System (ADS)

Rodriguez, Ana; Vazquez, Juan L.

The study of nonlinear diffusion equations produces a number of peculiar phenomena not present in the standard linear theory. Thus, in the sub-field of very fast diffusion it is known that the Cauchy problem can be ill-posed, either because of non-uniqueness, or because of non-existence of solutions with small data. The equations we consider take the general form ut=( D( u, ux) ux) x or its several-dimension analogue. Fast diffusion means that D→∞ at some values of the arguments, typically as u→0 or ux→0. Here, we describe two different types of non-existence phenomena. Some fast-diffusion equations with very singular D do not allow for solutions with sign changes, while other equations admit only monotone solutions, no oscillations being allowed. The examples we give for both types of anomaly are closely related. The most typical examples are vt=( vx/∣ v∣) x and ut= uxx/∣ ux∣. For these equations, we investigate what happens to the Cauchy problem when we take incompatible initial data and perform a standard regularization. It is shown that the limit gives rise to an initial layer where the data become admissible (positive or monotone, respectively), followed by a standard evolution for all t>0, once the obstruction has been removed.

Multi-Component Diffusion with Application To Computational Aerothermodynamics

NASA Technical Reports Server (NTRS)

Sutton, Kenneth; Gnoffo, Peter A.

1998-01-01

The accuracy and complexity of solving multicomponent gaseous diffusion using the detailed multicomponent equations, the Stefan-Maxwell equations, and two commonly used approximate equations have been examined in a two part study. Part I examined the equations in a basic study with specified inputs in which the results are applicable for many applications. Part II addressed the application of the equations in the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) computational code for high-speed entries in Earth's atmosphere. The results showed that the presented iterative scheme for solving the Stefan-Maxwell equations is an accurate and effective method as compared with solutions of the detailed equations. In general, good accuracy with the approximate equations cannot be guaranteed for a species or all species in a multi-component mixture. 'Corrected' forms of the approximate equations that ensured the diffusion mass fluxes sum to zero, as required, were more accurate than the uncorrected forms. Good accuracy, as compared with the Stefan- Maxwell results, were obtained with the 'corrected' approximate equations in defining the heating rates for the three Earth entries considered in Part II.

A Three-Fold Approach to the Heat Equation: Data, Modeling, Numerics

ERIC Educational Resources Information Center

Spayd, Kimberly; Puckett, James

2016-01-01

This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical…

A third-order computational method for numerical fluxes to guarantee nonnegative difference coefficients for advection-diffusion equations in a semi-conservative form

NASA Astrophysics Data System (ADS)

Sakai, K.; Watabe, D.; Minamidani, T.; Zhang, G. S.

2012-10-01

According to Godunov theorem for numerical calculations of advection equations, there exist no higher-order schemes with constant positive difference coefficients in a family of polynomial schemes with an accuracy exceeding the first-order. We propose a third-order computational scheme for numerical fluxes to guarantee the non-negative difference coefficients of resulting finite difference equations for advection-diffusion equations in a semi-conservative form, in which there exist two kinds of numerical fluxes at a cell surface and these two fluxes are not always coincident in non-uniform velocity fields. The present scheme is optimized so as to minimize truncation errors for the numerical fluxes while fulfilling the positivity condition of the difference coefficients which are variable depending on the local Courant number and diffusion number. The feature of the present optimized scheme consists in keeping the third-order accuracy anywhere without any numerical flux limiter. We extend the present method into multi-dimensional equations. Numerical experiments for advection-diffusion equations showed nonoscillatory solutions.

Novel Polyethylenimine–Acrylamide/SiO 2 Hybrid Hydrogel Sorbent for Rare-Earth-Element Recycling from Aqueous Sources

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Qiuming; Wilfong, Walter C.; Kail, Brian W.

Recycling rare earth elements (REEs) becomes increasingly important due to their supply vulnerability and increasing demands in industry, agriculture, and national security. Hybrid hydrogel sorbents were outstanding due to their high stability and selectivity. Organic-inorganic hybrid hydrogels were synthesized by thermo-polymerization of acrylamide onto PEI polymer chain with N,N’-methylene bisacrylamide as a crosslinker. The grafted network was evidenced by DRIFTS and XPS. The porous structure was observed by SEM. Crosslink degree, PEI grafting degree, and SiO 2 concentration were studied to optimize the REEs adsorption. The pH value of the medium greatly affected REE adsorption capacity, where the nearly neutralmore » conditions gave the strongest bonding of REEs to active sites. Moreover, kinetic studies showed that the rate-determining step of the adsorption process was chemical sorption, and that REE diffusion within micropores was the control step for, specifically, intraparticle diffusion. The adsorbents showed excellent selectivity and recyclability for REEs through 5 adsorption-desorption cycles in contact with synthetic acid mine drainage solution. A high separation toward REEs over fouling metals was achieved by using a citrate-based buffer eluent solution. This hybrid hydrogel shows promise for the recycling of REEs from aqueous solutions.« less

Novel Polyethylenimine–Acrylamide/SiO 2 Hybrid Hydrogel Sorbent for Rare-Earth-Element Recycling from Aqueous Sources

DOE PAGES

Wang, Qiuming; Wilfong, Walter C.; Kail, Brian W.; ...

2017-09-14

Recycling rare earth elements (REEs) becomes increasingly important due to their supply vulnerability and increasing demands in industry, agriculture, and national security. Hybrid hydrogel sorbents were outstanding due to their high stability and selectivity. Organic-inorganic hybrid hydrogels were synthesized by thermo-polymerization of acrylamide onto PEI polymer chain with N,N’-methylene bisacrylamide as a crosslinker. The grafted network was evidenced by DRIFTS and XPS. The porous structure was observed by SEM. Crosslink degree, PEI grafting degree, and SiO 2 concentration were studied to optimize the REEs adsorption. The pH value of the medium greatly affected REE adsorption capacity, where the nearly neutralmore » conditions gave the strongest bonding of REEs to active sites. Moreover, kinetic studies showed that the rate-determining step of the adsorption process was chemical sorption, and that REE diffusion within micropores was the control step for, specifically, intraparticle diffusion. The adsorbents showed excellent selectivity and recyclability for REEs through 5 adsorption-desorption cycles in contact with synthetic acid mine drainage solution. A high separation toward REEs over fouling metals was achieved by using a citrate-based buffer eluent solution. This hybrid hydrogel shows promise for the recycling of REEs from aqueous solutions.« less

Kinetics modelling of Cu(II) biosorption on to coconut shell and Moringa oleifera seeds from tropical regions.

PubMed

Acheampong, Mike A; Pereira, Joana P C; Meulepas, Roel J W; Lens, Piet N L

2012-01-01

Adsorption kinetic studies are of great significance in evaluating the performance of a given adsorbent and gaining insight into the underlying mechanism. This work investigated the sorption kinetics of Cu(II) on to coconut shell and Moringa oleifera seeds using batch techniques. To understand the mechanisms of the biosorption process and the potential rate-controlling steps, kinetic models were used to fit the experimental data. The results indicate that kinetic data were best described by the pseudo-second-order model with correlation coefficients (R2) of 0.9974 and 0.9958 for the coconut shell and Moringa oleifera seeds, respectively. The initial sorption rates obtained for coconut shell and Moringa oleifera seeds were 9.6395 x 10(-3) and 8.3292 x 10(-2) mg g(-1) min(-1), respectively. The values of the mass transfer coefficients obtained for coconut shell (1.2106 x 10(-3) cm s(-1)) and Moringa oleifera seeds (8.965 x 10(-4) cm s(-1)) indicate that the transport of Cu(II) from the bulk liquid to the solid phase was quite fast for both materials investigated. The results indicate that intraparticle diffusion controls the rate of sorption in this study; however, film diffusion cannot be neglected, especially at the initial stage of sorption.

Sorption behavior of nano-TiO2 for the removal of selenium ions from aqueous solution.

PubMed

Zhang, Lei; Liu, Na; Yang, Lijun; Lin, Qing

2009-10-30

Titanium dioxide nanoparticles were employed for the sorption of selenium ions from aqueous solution. The process was studied in detail by varying the sorption time, pH, and temperature. The sorption was found to be fast, and to reach equilibrium basically within 5.0 min. The sorption has been optimized with respect to the pH, maximum sorption has been achieved from solution of pH 2-6. Sorbed Se(IV) and Se(VI) were desorbed with 2.0 mL 0.1 mol L(-1) NaOH. The kinetics and thermodynamics of the sorption of Se(IV) onto nano-TiO2 have been studied. The kinetic experimental data properly correlate with the second-order kinetic model (k(2)=0.69 g mg(-1) min(-1), 293 K). The overall rate process appears to be influenced by both boundary layer diffusion and intraparticle diffusion. The sorption data could be well interpreted by the Langmuir sorption isotherm. The mean energy of adsorption (14.46 kJ mol(-1)) was calculated from the Dubinin-Radushkevich (D-R) adsorption isotherm at room temperature. The thermodynamic parameters for the sorption were also determined, and the DeltaH(0) and DeltaG(0) values indicate exothermic behavior.

Nitroimidazoles adsorption on activated carbon cloth from aqueous solution.

PubMed

Ocampo-Pérez, R; Orellana-Garcia, F; Sánchez-Polo, M; Rivera-Utrilla, J; Velo-Gala, I; López-Ramón, M V; Alvarez-Merino, M A

2013-07-01

The objective of this study was to analyze the equilibrium and adsorption kinetics of nitroimidazoles on activated carbon cloth (ACC), determining the main interactions responsible for the adsorption process and the diffusion mechanism of these compounds on this material. The influence of the different operational variables, such as ionic strength, pH, temperature, and type of water (ultrapure, surface, and waste), was also studied. The results obtained show that the ACC has a high capacity to adsorb nitroimidazoles in aqueous solution. Electrostatic interactions play an important role at pH<3, which favors the repulsive forces between dimetridazole or metronidazole and the ACC surface. The formation of hydrogen bonds and dispersive interactions play the predominant role at higher pH values. Modifications of the ACC with NH3, K2S2O8, and O3 demonstrated that its surface chemistry plays a predominant role in nitroimidazole adsorption on this material. The adsorption capacity of ACC is considerably high in surface waters and reduced in urban wastewater, due to the levels of alkalinity and dissolved organic matter present in the different types of water. Finally, the results of applying kinetic models revealed that the global adsorption rate of dimetridazole and metronidazole is controlled by intraparticle diffusion. Copyright © 2013 Elsevier Inc. All rights reserved.

Removing polycyclic aromatic hydrocarbons from water using granular activated carbon: kinetic and equilibrium adsorption studies.

PubMed

Eeshwarasinghe, Dinushika; Loganathan, Paripurnanda; Kalaruban, Mahatheva; Sounthararajah, Danious Pratheep; Kandasamy, Jaya; Vigneswaran, Saravanamuthu

2018-05-01

Polycyclic aromatic hydrocarbons (PAHs) constitute a group of highly persistent, toxic and widespread environmental micropollutants that are increasingly found in water. A study was conducted in removing five PAHs, specifically naphthalene, acenaphthylene, acenaphthene, fluorene and phenanthrene, from water by adsorption onto granular activated carbon (GAC). The pseudo-first-order (PFO) model satisfactorily described the kinetics of adsorption of the PAHs. The Weber and Morris diffusion model's fit to the data showed that there were faster and slower rates of intra-particle diffusion probably into the mesopores and micropores of the GAC, respectively. These rates were negatively related to the molar volumes of the PAHs. Batch equilibrium adsorption data fitted well to the Langmuir, Freundlich and Dubinin-Radushkevich models, of which the Freundlich model exhibited the best fit. The adsorption affinities were related to the hydrophobicity of the PAHs as determined by the log K ow values. Free energies of adsorption calculated from the Dubinin-Radushkevich model and the satisfactory kinetic data fitting to the PFO model suggested physical adsorption of the PAHs. Adsorption of naphthalene, acenaphthylene and acenaphthene in fixed-bed columns containing a mixture of GAC (0.5 g) + sand (24.5 g) was satisfactorily simulated by the Thomas model.

Biosorption of metal ions using a low cost modified adsorbent (Mauritia flexuosa): experimental design and mathematical modeling.

PubMed

Melo, Diego de Quadros; Vidal, Carla Bastos; Medeiros, Thiago Coutinho; Raulino, Giselle Santiago Cabral; Dervanoski, Adriana; Pinheiro, Márcio do Carmo; Nascimento, Ronaldo Ferreira do

2016-09-01

Buriti fibers were subjected to an alkaline pre-treatment and tested as an adsorbent to investigate the adsorption of copper, cadmium, lead and nickel in mono- and multi-element aqueous solutions, the results showed an increase in the adsorption capacity compared to the unmodified Buriti fiber. The effects of pH, adsorbent mass, agitation rate and initial metal ions concentration on the efficiency of the adsorption process were studied using a fractional 2(4-1) factorial design, and the results showed that all four parameters influenced metal adsorption differently. Fourier transform infrared spectrometry and X-ray fluorescence analysis were used to identify the groups that participated in the adsorption process and suggest its mechanisms and they indicated the probable mechanisms involved in the adsorption process are mainly ion exchange. Kinetic and thermodynamic equilibrium parameters were determined. The adsorption kinetics were adjusted to the homogeneous diffusion model. The adsorption equilibrium was reached in 30 min for Cu(2+) and Pb(2+), 20 min for Ni(2+) and instantaneously for Cd(2+). The results showed a significant difference was found in the competitiveness for the adsorption sites. A mathematical model was used to simulate the breakthrough curves in multi-element column adsorption considering the influences of external mass transfer and intraparticle diffusion resistance.

Adsorption kinetic and desorption studies of Cd2+ on Multi-Carboxylic-Functionalized Silica Gel

NASA Astrophysics Data System (ADS)

Li, Min; Wei, Jian; Meng, Xiaojing; Wu, Zhuqiang; Liang, Xiuke

2018-01-01

In the present study, the adsorption behavior of cadmium (II) ion from aqueous solution onto multi-carboxylic-functionalized silica gel (SG-MCF) has been investigated in detail by means of batch and column experiments. Batch experiments were performed to evaluate the effects of contact time on adsorption capacity of cadmium (II) ion. The kinetic data were analyzed on the basis of the pseudo-first-order kinetic and the pseudo-second-order kinetic models and consequently, the pseudo-second-order kinetic can better describe the adsorption process than the pseudo-first-order kinetic model. And the adsorption mechanism of the process was studied by intra-particle and film diffusion, it was found out that the adsorption rate was governed primarily by film diffusion to the adsorption onto the SG-MCF. In addition, column experiments were conducted to assess the effects initial inlet concentration and the flow rate on breakthrough time and adsorption capacity ascertaining the practical applicability of the adsorbent. The results suggest that the total amount of adsorbed cadmium (II) ion increased with declined flow rate and increased the inlet concentration. The adsorption-desorption experiment confirmed that adsorption capacity of cadmium (II) ion didn’t present an obvious decrease after five cycles.

Adsorption kinetic and desorption studies of Cu2+ on Multi-Carboxylic-Functionalized Silica Gel

NASA Astrophysics Data System (ADS)

Li, Min; Meng, Xiaojing; Liu, Yushuang; Hu, Xinju; Liang, Xiuke

2018-01-01

In the present study, the adsorption behavior of copper (II) ion from aqueous solution onto multi-carboxylic-functionalized silica gel (SG-MCF) has been investigated in detail by means of batch and column experiments. Batch experiments were performed to evaluate the effects of contact time on adsorption capacity of copper (II) ion. The kinetic data were analyzed on the basis of the pseudo-first-order kinetic and the pseudo-second-order kinetic models and consequently, the pseudo-second-order kinetic can better describe the adsorption process than the pseudo-first-order kinetic model. And the adsorption mechanism of the process was studied by intra-particle and film diffusion, it was found out that the adsorption rate was governed primarily by film diffusion to the adsorption onto the SG-MCF. In addition, column experiments were conducted to assess the effects initial inlet concentration and the flow rate on breakthrough time and adsorption capacity ascertaining the practical applicability of the adsorbent. The results suggest that the total amount of adsorbed copper (II) ion increased with declined flow rate and increased the inlet concentration. The adsorption-desorption experiment confirmed that adsorption capacity of copper (II) ion didn’t present an obvious decrease after five cycles.

Global Regularity and Time Decay for the 2D Magnetohydrodynamic Equations with Fractional Dissipation and Partial Magnetic Diffusion

NASA Astrophysics Data System (ADS)

Dong, Bo-Qing; Jia, Yan; Li, Jingna; Wu, Jiahong

2018-05-01

This paper focuses on a system of the 2D magnetohydrodynamic (MHD) equations with the kinematic dissipation given by the fractional operator (-Δ )^α and the magnetic diffusion by partial Laplacian. We are able to show that this system with any α >0 always possesses a unique global smooth solution when the initial data is sufficiently smooth. In addition, we make a detailed study on the large-time behavior of these smooth solutions and obtain optimal large-time decay rates. Since the magnetic diffusion is only partial here, some classical tools such as the maximal regularity property for the 2D heat operator can no longer be applied. A key observation on the structure of the MHD equations allows us to get around the difficulties due to the lack of full Laplacian magnetic diffusion. The results presented here are the sharpest on the global regularity problem for the 2D MHD equations with only partial magnetic diffusion.

Isotherm and kinetic studies on adsorption of oil sands process-affected water organic compounds using granular activated carbon.

PubMed

Islam, Md Shahinoor; McPhedran, Kerry N; Messele, Selamawit A; Liu, Yang; Gamal El-Din, Mohamed

2018-07-01

The production of oil from oil sands in northern Alberta has led to the generation of large volumes of oil sands process-affected water (OSPW) that was reported to be toxic to aquatic and other living organisms. The toxicity of OSPW has been attributed to the complex nature of OSPW matrix including the inorganic and organic compounds primarily naphthenic acids (NAs: C n H 2n+Z O x ). In the present study, granular activated carbon (GAC) adsorption was investigated for its potential use to treat raw and ozonated OSPW. The results indicated that NA species removal increased with carbon number (n) for a fixed Z number; however, the NA species removal decreased with Z number for a fixed carbon number. The maximum adsorption capacities obtained from Langmuir adsorption isotherm based on acid-extractable fraction (AEF) and NAs were 98.5 mg and 60.9 mg AEF/g GAC and 60 mg and 37 mg NA/g GAC for raw and ozonated OSPW, respectively. It was found that the Freundlich isotherm model best fits the AEF and NA equilibrium data (r 2  ≥ 0.88). The adsorption kinetics showed that the pseudo-second order and intraparticle diffusion models were both appropriate in modeling the adsorption kinetics of AEF and NAs to GAC (r 2  ≥ 0.97). Although pore diffusion was the rate limiting step, film diffusion was still significant for assessing the rate of diffusion of NAs. This study could be helpful to model, design and optimize the adsorption treatment technologies of OSPW and to assess the performance of other adsorbents. Copyright © 2018 Elsevier Ltd. All rights reserved.

Fisher equation for anisotropic diffusion: simulating South American human dispersals.

PubMed

Martino, Luis A; Osella, Ana; Dorso, Claudio; Lanata, José L

2007-09-01

The Fisher equation is commonly used to model population dynamics. This equation allows describing reaction-diffusion processes, considering both population growth and diffusion mechanism. Some results have been reported about modeling human dispersion, always assuming isotropic diffusion. Nevertheless, it is well-known that dispersion depends not only on the characteristics of the habitats where individuals are but also on the properties of the places where they intend to move, then isotropic approaches cannot adequately reproduce the evolution of the wave of advance of populations. Solutions to a Fisher equation are difficult to obtain for complex geometries, moreover, when anisotropy has to be considered and so few studies have been conducted in this direction. With this scope in mind, we present in this paper a solution for a Fisher equation, introducing anisotropy. We apply a finite difference method using the Crank-Nicholson approximation and analyze the results as a function of the characteristic parameters. Finally, this methodology is applied to model South American human dispersal.

Viscous regularization of the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations

DOE PAGES

Delchini, Marc O.; Ragusa, Jean C.; Ferguson, Jim

2017-02-17

A viscous regularization technique, based on the local entropy residual, was proposed by Delchini et al. (2015) to stabilize the nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations using an artificial viscosity technique. This viscous regularization is modulated by the local entropy production and is consistent with the entropy minimum principle. However, Delchini et al. (2015) only based their work on the hyperbolic parts of the Grey Radiation-Hydrodynamic equations and thus omitted the relaxation and diffusion terms present in the material energy and radiation energy equations. Here in this paper, we extend the theoretical grounds for the method and derive an entropy minimum principlemore » for the full set of nonequilibrium-diffusion Grey Radiation-Hydrodynamic equations. This further strengthens the applicability of the entropy viscosity method as a stabilization technique for radiation-hydrodynamic shock simulations. Radiative shock calculations using constant and temperature-dependent opacities are compared against semi-analytical reference solutions, and we present a procedure to perform spatial convergence studies of such simulations.« less

Localization and Ballistic Diffusion for the Tempered Fractional Brownian-Langevin Motion

NASA Astrophysics Data System (ADS)

Chen, Yao; Wang, Xudong; Deng, Weihua

2017-10-01

This paper discusses the tempered fractional Brownian motion (tfBm), its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tfBm displays localization diffusion for the long time limit and for the short time its mean squared displacement (MSD) has the asymptotic form t^{2H}, we show that the asymptotic form of the MSD of the tfLe transits from t^2 (ballistic diffusion for short time) to t^{2-2H}, and then to t^2 (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from t^{2-2H} to t^2 (ballistic diffusion). The tfLe with harmonic potential is also considered.

A Nonlinear Diffusion Equation-Based Model for Ultrasound Speckle Noise Removal

NASA Astrophysics Data System (ADS)

Zhou, Zhenyu; Guo, Zhichang; Zhang, Dazhi; Wu, Boying

2018-04-01

Ultrasound images are contaminated by speckle noise, which brings difficulties in further image analysis and clinical diagnosis. In this paper, we address this problem in the view of nonlinear diffusion equation theories. We develop a nonlinear diffusion equation-based model by taking into account not only the gradient information of the image, but also the information of the gray levels of the image. By utilizing the region indicator as the variable exponent, we can adaptively control the diffusion type which alternates between the Perona-Malik diffusion and the Charbonnier diffusion according to the image gray levels. Furthermore, we analyze the proposed model with respect to the theoretical and numerical properties. Experiments show that the proposed method achieves much better speckle suppression and edge preservation when compared with the traditional despeckling methods, especially in the low gray level and low-contrast regions.

Nature of self-diffusion in two-dimensional fluids

NASA Astrophysics Data System (ADS)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; Talkner, Peter; Kidera, Akinori; Lee, Eok Kyun

2017-12-01

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. We numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(t\\sqrt{{ln}t}), however with a rescaled time.

Dimensional reduction of a general advection–diffusion equation in 2D channels

NASA Astrophysics Data System (ADS)

Kalinay, Pavol; Slanina, František

2018-06-01

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick–Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient can be always found.

Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

NASA Astrophysics Data System (ADS)

Li, Linling; Wang, Xiaoliang; Zhou, Dongshan; Xue, Gi

2013-03-01

We report a diffusion study on the polystyrene/poly(phenylene oxide) (PS/PPO) mixture consisted by the PS and PPO nanoparticles. Diffusion of liquid PS into glassy PPO (l-PS/g-PPO) is promoted by annealing the PS/PPO mixture at several temperatures below Tg of the PPO. By tracing the Tgs of the PS-rich domain behind the diffusion front using DSC, we get the relationships of PS weight fractions and diffusion front advances with the elapsed diffusion times at different diffusion temperatures using the Gordon-Taylor equation and core-shell model. We find that the plots of weight fraction of PS vs. elapsed diffusion times at different temperatures can be converted to a master curve by Time-Temperature superposition, and the shift factors obey the Arrhenius equation. Besides, the diffusion front advances of l-PS into g-PPO show an excellent agreement with the t1/2 scaling law at the beginning of the diffusion process, and the diffusion coefficients of different diffusion temperatures also obey the Arrhenius equation. We believe the diffusion mechanism for l-PS/g-PPO should be the Fickean law rather than the Case II, though there are departures of original linearity at longer diffusion times due to the limited liquid supply system. Diffusion of liquid polystyrene into glassy poly(phenylene oxide) characterized by DSC

Vapor Transport Within the Thermal Diffusion Cloud Chamber

NASA Technical Reports Server (NTRS)

Ferguson, Frank T.; Heist, Richard H.; Nuth, Joseph A., III

2000-01-01

A review of the equations used to determine the 1-D vapor transport in the thermal diffusion cloud chamber (TDCC) is presented. These equations closely follow those of the classical Stefan tube problem in which there is transport of a volatile species through a noncondensible, carrier gas. In both cases, the very plausible assumption is made that the background gas is stagnant. Unfortunately, this assumption results in a convective flux which is inconsistent with the momentum and continuity equations for both systems. The approximation permits derivation of an analytical solution for the concentration profile in the Stefan tube, but there is no computational advantage in the case of the TDCC. Furthermore, the degree of supersaturation is a sensitive function of the concentration profile in the TD CC and the stagnant background gas approximation can make a dramatic difference in the calculated supersaturation. In this work, the equations typically used with a TDCC are compared with very general transport equations describing the 1-D diffusion of the volatile species. Whereas no pressure dependence is predicted with the typical equations, a strong pressure dependence is present with the more general equations given in this work. The predicted behavior is consistent with observations in diffusion cloud experiments. It appears that the new equations may account for much of the pressure dependence noted in TDCC experiments, but a comparison between the new equations and previously obtained experimental data are needed for verification.

Boundary particle method for Laplace transformed time fractional diffusion equations

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Yang, Hai-Tian

2013-02-01

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Laplace-transformed problem. Unlike the other boundary discretization methods, the BPM does not require any inner nodes, since the recursive composite multiple reciprocity technique (RC-MRM) is used to convert the inhomogeneous problem into the higher-order homogeneous problem. Finally, the Stehfest numerical inverse Laplace transform (NILT) is implemented to retrieve the numerical solutions of time fractional diffusion equations from the corresponding BPM solutions. In comparison with finite difference discretization, the LTBPM introduces Laplace transform and Stehfest NILT algorithm to deal with time fractional derivative term, which evades costly convolution integral calculation in time fractional derivation approximation and avoids the effect of time step on numerical accuracy and stability. Consequently, it can effectively simulate long time-history fractional diffusion systems. Error analysis and numerical experiments demonstrate that the present LTBPM is highly accurate and computationally efficient for 2D and 3D time fractional diffusion equations.

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

DOE PAGES

Chang, Justin; Karra, Satish; Nakshatrala, Kalyana B.

2016-07-26

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, usedmore » for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.« less

Ionic Channels as Natural Nanodevices

DTIC Science & Technology

2006-05-01

introduce the numerical techniques required to simulate charge transport in ion channels. [1] Using Poisson- Nernst -Planck-type (PNP) equations ...Eisenberg. 2003. Ionic diffusion through protein channels: from molecular description to continuum equations . Nanotech 2003, 3: 439-442. 4...Nadler, B., Schuss, Z., Singer, A., and R. S. Eisenberg. 2004. Ionic diffusion through confined geometries: from Langevin equations to partial

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

NASA Astrophysics Data System (ADS)

Cairoli, Andrea; Baule, Adrian

2017-04-01

Functionals of a stochastic process Y(t) model many physical time-extensive observables, for instance particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the celebrated Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is non-Brownian, e.g. an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is directly related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in numerous experiments on biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are of particular relevance for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. An additional aim of this paper is to provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

FDM study of ion exchange diffusion equation in glass

NASA Astrophysics Data System (ADS)

Zhou, Zigang; Yang, Yongjia; Wang, Qiang; Sun, Guangchun

2009-05-01

Ion-exchange technique in glass was developed to fabricate gradient refractive index optical devices. In this paper, the Finite Difference Method(FDM), which is used for the solution of ion-diffusion equation, is reported. This method transforms continual diffusion equation to separate difference equation. It unitizes the matrix of MATLAB program to solve the iteration process. The collation results under square boundary condition show that it gets a more accurate numerical solution. Compared to experiment data, the relative error is less than 0.2%. Furthermore, it has simply operation and kinds of output solutions. This method can provide better results for border-proliferation of the hexagonal and the channel devices too.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

NASA Astrophysics Data System (ADS)

Hosseini, Kamyar; Mayeli, Peyman; Bekir, Ahmet; Guner, Ozkan

2018-01-01

In this article, a special type of fractional differential equations (FDEs) named the density-dependent conformable fractional diffusion-reaction (DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the \\exp (-φ (\\varepsilon )) -expansion and modified Kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

A Simple, Analytical Model of Collisionless Magnetic Reconnection in a Pair Plasma

NASA Technical Reports Server (NTRS)

Hesse, Michael; Zenitani, Seiji; Kuznetova, Masha; Klimas, Alex

2011-01-01

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region, and to impart thermal energy to the plasma by means of quasi-viscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative, procedure. The solutions show expected features such as dominance of enthalpy flux in the reconnection outflow, as well as combination of adiabatic and quasi-viscous heating. Furthermore, the model predicts a maximum reconnection electric field of E(sup *)=0.4, normalized to the parameters at the inflow edge of the diffusion region.

A simple, analytical model of collisionless magnetic reconnection in a pair plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha

2009-10-15

A set of conservation equations is utilized to derive balance equations in the reconnection diffusion region of a symmetric pair plasma. The reconnection electric field is assumed to have the function to maintain the current density in the diffusion region and to impart thermal energy to the plasma by means of quasiviscous dissipation. Using these assumptions it is possible to derive a simple set of equations for diffusion region parameters in dependence on inflow conditions and on plasma compressibility. These equations are solved by means of a simple, iterative procedure. The solutions show expected features such as dominance of enthalpymore » flux in the reconnection outflow, as well as combination of adiabatic and quasiviscous heating. Furthermore, the model predicts a maximum reconnection electric field of E{sup *}=0.4, normalized to the parameters at the inflow edge of the diffusion region.« less

Comparison of fluid neutral models for one-dimensional plasma edge modeling with a finite volume solution of the Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M.; Dekeyser, W.

2016-01-15

We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assumingmore » equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.« less

Symmetry Reductions of Fourth-Order Nonlinear Diffusion Equations: Lubrication Model and Some Generalizations

NASA Astrophysics Data System (ADS)

Gandarias, M. L.; Medina, E.

Fourth-order nonlinear diffusion equations appear frequently in the description of physical processes, among these, the lubrication equation ut = (unuxxxx)x or the corresponding modified version ut = unuxxxx play an important role in the study of the interface movements. In this work we analyze the generalizations of the above equations given by ut = (f(u)uxxxx)x, ut = (f(u)uxxxx, and we find that if f(u) = un or f(u) = e-u the equations admit extra classical symmetries. The corresponding reductions are performed and some solutions are characterized.

Wave and pseudo-diffusion equations from squeezed states

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1993-01-01

We show that the probability distributions P(sub n)(q,p;y) := the absolute value squared of (n(p,q;y), which are obtained from squeezed states, obey an interesting partial differential equation, to which we give two intuitive interpretations: as a wave equation in one space dimension; and as a pseudo-diffusion equation. We also study the corresponding Wehrl entropies S(sub n)(y), and we show that they have minima at zero squeezing, y = 0.

Gravitational instability of filamentary molecular clouds, including ambipolar diffusion; non-isothermal filament

NASA Astrophysics Data System (ADS)

Hosseinirad, Mohammad; Abbassi, Shahram; Roshan, Mahmood; Naficy, Kazem

2018-04-01

Recent observations of the filamentary molecular clouds show that their properties deviate from the isothermal equation of state. Theoretical investigations proposed that the logatropic and the polytropic equations of state with negative indexes can provide a better description for these filamentary structures. Here, we aim to compare the effects of these softer non-isothermal equations of state with their isothermal counterpart on the global gravitational instability of a filamentary molecular cloud. By incorporating the ambipolar diffusion, we use the non-ideal magnetohydrodynamics framework for a filament that is threaded by a uniform axial magnetic field. We perturb the fluid and obtain the dispersion relation both for the logatropic and polytropic equations of state by taking the effects of magnetic field and ambipolar diffusion into account. Our results suggest that, in absence of the magnetic field, a softer equation of state makes the system more prone to gravitational instability. We also observed that a moderate magnetic field is able to enhance the stability of the filament in a way that is sensitive to the equation of state in general. However, when the magnetic field is strong, this effect is suppressed and all the equations of state have almost the same stability properties. Moreover, we find that for all the considered equations of state, the ambipolar diffusion has destabilizing effects on the filament.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Rod-shaped silica particles derivatized with elongated silver nanoparticles immobilized within mesopores

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mnasri, Najib; Materials, Environment and Energy Laboratory; Charnay, Clarence

Silver-derivatized silica particles possessing a non-spherical morphology and surface plasmon resonance properties have been achieved. Nanometer-sized silica rods with uniformly sized mesopore channels were prepared first making use of alkyltrimethyl ammonium surfactants as porogens and the 1:0.10 tetraethyl orthosilicate (TEOS) : 3-aminopropyltriethoxysilane (APTES) mixture as a silicon source. Silica rods were subsequently functionalized by introducing elongated silver nanoparticles within the intra-particle mesopores thanks to the AgNO{sub 3} reduction procedure based on the action of hemiaminal groups previously located on the mesopore walls. The textural and structural features of the samples were inferred from the combined characterization studies including SEM andmore » TEM microscopy, nitrogen adsorption-desorption at 77 K, powder XRD in the small- and wide-angle region, as well as UV–visible spectroscopy. {sup 129}Xe NMR spectroscopy appeared particularly useful to obtain a correct information about the porous structure of rod-shaped silica particles and the silver incorporation within their intra-particle mesopores. - Highlights: • Mesoporous monodisperse submicron-sized silica rods were achieved. • Silver nanoparticles were located lengthwise within the intra-particle mesopores. • Textural and plasmonic properties of particles studied by {sup 129}Xe NMR and UV–Vis.« less

Performance of the fixed-bed of granular activated carbon for the removal of pesticides from water supply.

PubMed

Alves, Alcione Aparecida de Almeida; Ruiz, Giselle Louise de Oliveira; Nonato, Thyara Campos Martins; Müller, Laura Cecilia; Sens, Maurício Luiz

2018-02-26

The application of a fixed bed adsorption column of granular activated carbon (FBAC-GAC), in the removal of carbaryl, methomyl and carbofuran at a concentration of 25 μg L -1 for each carbamate, from the public water supply was investigated. For the determination of the presence of pesticides in the water supply, the analytical technique of high-performance liquid chromatography with post-column derivatization was used. Under conditions of constant diffusivity, the FBAC-GAC was saturated after 196 h of operation on a pilot scale. The exhaust rate of the granular activated carbon (GAC) in the FBAC-GAC until the point of saturation was 0.02 kg GAC m -3 of treated water. By comparing a rapid small-scale column test and FBAC-GAC, it was confirmed that the predominant intraparticle diffusivity in the adsorption column was constant diffusivity. Based on the results obtained on a pilot scale, it was possible to estimate the values to be applied in the FBAC-GAC (full scale) to remove the pesticides, which are particle size with an average diameter of 1.5 mm GAC; relationship between the internal diameter of the column and the average diameter of GAC ≥50 in order to avoid preferential flow near the adsorption column wall; surface application rate 240 m 3  m -2  d -1 and an empty bed contact time of 3 min. BV: bed volume; CD: constant diffusivity; EBCT: empty bed contact time; FBAC-GAC: fixed bed adsorption column of granular activated carbon; GAC: granular activated carbon; MPV: maximum permitted values; NOM: natural organic matter; PD: proportional diffusivity; pH PCZ : pH of the zero charge point; SAR: surface application rate; RSSCT: rapid small-scale column test; WTCS: water treated conventional system.

The effects of surface chemistry of mesoporous silica materials and solution pH on kinetics of molsidomine adsorption

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dolinina, E.S.; Parfenyuk, E.V., E-mail: terrakott37@mail.ru

2014-01-15

Adsorption kinetics of molsidomine on mesoporous silica material (UMS), the phenyl- (PhMS) and mercaptopropyl-functionalized (MMS) derivatives from solution with different pH and 298 K was studied. The adsorption kinetics was found to follow the pseudo-second-order kinetic model for all studied silica materials and pH. Effects of surface functional groups and pH on adsorption efficiency and kinetic adsorption parameters were investigated. At all studied pH, the highest molsidomine amount is adsorbed on PhMS due to π–π interactions and hydrogen bonding between surface groups of PhMS and molsidomine molecules. An increase of pH results in a decrease of the amounts of adsorbedmore » molsidomine onto the silica materials. Furthermore, the highest adsorption rate kinetically evaluated using a pseudo-second-order model, is observed onto UMS and it strongly depends on pH. The mechanism of the adsorption process was determined from the intraparticle diffusion and Boyd kinetic film–diffusion models. The results showed that the molsidomine adsorption on the silica materials is controlled by film diffusion. Effect of pH on the diffusion parameters is discussed. - Graphical abstract: The kinetic study showed that the k{sub 2} value, the rate constant of pseudo-second order kinetic model, is the highest for molsidomine adsorption on UMS and strongly depends on pH because it is determined by availability and accessibility of the reaction sites of the adsorbents molsidomine binding. Display Omitted - Highlights: • The adsorption capacities of UMS, PhMS and MMS were dependent on the pH. • At all studied pH, the highest molsidomine amount is adsorbed on PhMS. • The highest adsorption rate, k{sub 2}, is observed onto UMS and strongly depends on pH. • Film diffusion was the likely rate-limiting step in the adsorption process.« less

Sorption kinetics of zinc and nickel on modified chitosan.

PubMed

Tripathi, Nimisha; Choppala, Girish; Singh, Raj S; Srivastava, Prashant; Seshadri, Balaji

2016-09-01

This study was conducted to evaluate the effect of equilibration time on adsorption of zinc [Zn(II)] and nickel [Ni(II)] on pure and modified chitosan beads. The initial adsorption of Zn(II) was high on molybdenum (Mo)-impregnated chitosan beads (MoCB) during the initial 60 min. However, after 240 min, Zn(II) adsorption occurred more on single super phosphate chitosan beads (SSPCB), followed by monocalcium phosphate chitosan beads (MCPCB), untreated pure chitosan beads (UCB), and MoCB. Similarly, Ni(II) adsorption was greatest on MoCB during the initial 60 min. At the conclusion of the experiment (at 240 min), the greatest adsorption was occurred on MCPCB, followed by MoCB, UCB, and SSPCB. Chemical sorption and intra-particle diffusion were probably the dominant processes responsible for Zn(II) and Ni(II) sorption onto chitosan beads. The results demonstrated that modified chitosan beads were effective in adsorbing Zn and Ni and hence, could be used for the removal of these toxic metals from soil.

Comparative evaluation of sorption kinetics and isotherms of pyrene onto microplastics.

PubMed

Wang, Wenfeng; Wang, Jun

2018-02-01

Concerns regarding microplastics pollution and their potential to concentrate and transport organic contaminants in aquatic environments are growing in recent years. Sorption of organic chemicals by microplastics may affect the distribution and bioavailability of the chemicals. Here sorption process of pyrene (Pyr), a frequently encountered polycyclic aromatic hydrocarbon in aquatic environments, on three types of mass-produced plastic particles (high-density polyethylene (PE), polystyrene (PS) and polyvinylchloride (PVC)), was investigated by comparative analysis of different sorption kinetic and isotherm models. Optimum kinetic and isotherm models were predicted by the linear least-squares regression method. The pseudo-second-order kinetic model was more appropriate in describing the entire sorption process (R 2  > 0.99). Sorption rates of Pyr onto microplastics were mainly controlled by intraparticle diffusion. PE exhibited the highest affinity for Pyr, followed by PS and PVC. The sorption equilibrium data were best fitted to the Langmuir isotherm (R 2  > 0.99), indicating monolayer coverage of Pyr onto the microplastics. Copyright © 2017 Elsevier Ltd. All rights reserved.

Kinetic and morphology study of alginate-vineyard pruning waste biocomposite vs. non modified vineyard pruning waste for dye removal.

PubMed

Vecino, Xanel; Devesa-Rey, Rosa; Villagrasa, Salvador; Cruz, Jose M; Moldes, Ana B

2015-12-01

In this work a comparative bioadsorption study between a biocomposite consisting of hydrolysed vineyard pruning waste entrapped in calcium alginate spheres and non entrapped vineyard residue was carried out. Results have demonstrated that the biocomposite based on lignocellulose-calcium alginate spheres removed 77.3% of dyes, while non entrapped lignocellulose eliminated only removed 27.8% of colour compounds. The experimental data were fitted to several kinetic models (pseudo-first order, pseudo-second order, Chien-Clayton model, intraparticle diffusion model and Bangham model); being pseudo-second order the kinetic model that better described the adsorption of dyes onto both bioadsorbents. In addition, a morphological study (roughness and shape) of alginate-vineyard biocomposite was established under extreme conditions, observing significant differences between hydrated and dehydrated alginate-vineyard biocomposite. The techniques used to carry out this morphological study consisted of scanning electron microscopy (SEM), perfilometry and 3D surface analysis. Copyright © 2015. Published by Elsevier B.V.

Adsorption kinetics, isotherms and thermodynamics of atrazine removal using a banana peel based sorbent.

PubMed

Chaparadza, Allen; Hossenlopp, Jeanne M

2012-01-01

Atrazine removal from water by treated banana peels was studied. The effect of pH, contact time, initial atrazine concentration, and temperature were investigated. Batch experiments demonstrated that 15 g L(-1) adsorbent dosage removed 90-99% of atrazine from 1-150 ppm aqueous solutions. The removal was both pH and temperature dependent with the most atrazine removed between pH 7 and 8.2 and increased with increasing temperature. Equilibrium data fitted well to the Langmuir and Redlich-Peterson models in the concentration and temperature ranges investigated, with a maximum adsorption capacity of 14 mg g(-1). Simple mass transfer models were applied to the experimental data to examine the adsorption mechanism and it was found that both external mass transfer and intraparticle diffusion played important roles in the adsorption mechanisms. The enthalpy of atrazine adsorption was evaluated to be 67.8 ± 6.3 kJ mol(-l) with a Gibbs free energy of -5.7 ± 1.2 kJ mol(-1).

Distribution and removal of organochlorine pesticides in waste clay bricks from an abandoned manufacturing plant using low-temperature thermal desorption technology.

PubMed

Cong, Xin; Li, Fasheng; Kelly, Ryan M; Xue, Nandong

2018-04-01

The distribution of pollutants in waste clay bricks from an organochlorine pesticide-contaminated site was investigated, and removal of the pollutants using a thermal desorption technology was studied. The results showed that the contents of HCHs in both the surface and the inner layer of the bricks were slightly higher than those of DDTs. The total pore volume of the bricks was 37.7 to 41.6% with an increase from external to internal surfaces. The removal efficiency by thermal treatment was within 62 to 83% for HCHs and DDTs in bricks when the temperature was raised from 200 to 250 °C after 1 h. HCHs were more easily removed than DDTs with a higher temperature. Either intraparticle or surface diffusion controls the desorption processes of pollutants in bricks. It was feasible to use the polluted bricks after removal of the pollutants by low-temperature thermal desorption technology.

Carbon composite lignin-based adsorbents for the adsorption of dyes.

PubMed

Wang, Xiaohong; Jiang, Chenglong; Hou, Bingxia; Wang, Yingying; Hao, Chen; Wu, Jingbo

2018-05-10

Carbon composite lignin-based adsorbent were prepared through hydrothermal method with glucose as carbon source, calcium lignosulfonate and triethylene tetramine as raw materials, respectively. The optimum synthesis conditions were determined by investigating the addition of carbon and triethylene tetramine. The adsorbent was used for the adsorption of azo dyes Congo red and Eriochrome blue black R, and the five factors affecting the adsorption were discussed, including pH of dyes, initial concentration, adsorption time, adsorption temperature and adsorbent dosage. The corresponding adsorption mechanism such as pseudo first order kinetics, pseudo second order kinetics, intraparticle diffusion, Langmuir adsorption isotherm, Freundlich isotherm, Temkin isotherm, Dubinin-Radushkevich adsorption isotherm, thermodynamics were also studied. When the dye concentration is 40 mg L -1 , Congo red and Eriochrome blue black R dye removal rates reach 99%. Moreover, the adsorption process of two kinds of dyes follow the pseudo second order kinetics and the Langmuir adsorption isotherm. Copyright © 2018 Elsevier Ltd. All rights reserved.

Jute stick powder as a potential biomass for the removal of congo red and rhodamine B from their aqueous solution.

PubMed

Panda, Gopal C; Das, Sujoy K; Guha, Arun K

2009-05-15

Jute stick powder (JSP) has been found to be a promising material for adsorptive removal of congo red (C.I. 22120) and rhodamine B (C.I. 45170) from aqueous solutions. Physico-chemical parameters like dye concentration, solution pH, temperature and contact time have been varied to study the adsorption phenomenon. Favorable adsorption occurs at around pH 7.0 whereas temperature has no significant effect on adsorption of both the dyes. The maximum adsorption capacity has been calculated to be 35.7 and 87.7mg/g of the biomass for congo red and rhodamine B, respectively. The adsorption process is in conformity with Freundlich and Langmuir isotherms for rhodamine B whereas congo red adsorption fits well to Langmuir isotherm only. In both the cases, adsorption occurs very fast initially and attains equilibrium within 60min. Kinetic results suggest the intra-particle diffusion of dyes as rate limiting step.

Lead and vanadium removal from a real industrial wastewater by gravitational settling/sedimentation and sorption onto Pinus sylvestris sawdust.

PubMed

Kaczala, F; Marques, M; Hogland, W

2009-01-01

Batch sorption with untreated Pinus sylvestris sawdust after settling/sedimentation phase to remove vanadium and lead from a real industrial wastewater was investigated using different adsorbent doses, initial pH, and contact time. The development of pH along the sorption test and a parallel investigation of metals release from sawdust in distilled water were carried out. In order to evaluate kinetic parameters and equilibrium isotherms, Lagergren first-order, pseudo-second-order, intra-particle diffusion and Freundlich models were explored. When the initial pH was reduced from 7.4 to 4.0, the sorption efficiency increased from 32% to 99% for Pb and from 43% to 95% for V. Whereas, V removal was positively correlated with the adsorbent dose, Pb removal was not. The sorption process was best described by pseudo-second-order kinetics. According to Freundlich parameters (K(f) and n) sawdust presented unfavourable intensity for sorption of V.

Peach gum for efficient removal of methylene blue and methyl violet dyes from aqueous solution.

PubMed

Zhou, Li; Huang, Jiachang; He, Benzhao; Zhang, Faai; Li, Huabin

2014-01-30

This study investigated the potential use of natural peach gum (PG) as alternative adsorbent for the removal of dyes from aqueous solutions. The PG showed high adsorption capacities and selectivity for cationic dyes (e.g., methylene blue (MB) and methyl violet (MV)) in the pH range 6-10. 98% of MB and MV could be adsorbed within 5 min, and both of the adsorptions reached equilibrium within 30 min. The dye uptake process followed the pseudo-second-order kinetic model. The intraparticle diffusion was not the sole rate controlling step. Equilibrium adsorption isotherm data indicated a good fit to the Langmuir isotherm model. Regeneration study revealed that PG could be well regenerated in acid solution. The recovered PG still exhibited high adsorption capacity even after five cycles of desorption-adsorption. On the basis of its excellent adsorption performance and facile availability, PG can be employed as an efficient low cost adsorbent for environmental cleanup. Copyright © 2013 Elsevier Ltd. All rights reserved.

Effective removal of Congo red dye from aqueous solution using modified xanthan gum/silica hybrid nanocomposite as adsorbent.

PubMed

Ghorai, Soumitra; Sarkar, Amit Kumar; Panda, A B; Pal, Sagar

2013-09-01

The aim of this work is to study the feasibility of XG-g-PAM/SiO2 nanocomposite towards its potential application as high performance adsorbent for removal of Congo red (CR) dye from aqueous solution. The surface area, average pore size and total pore volume of the developed nanocomposite has been determined. The efficiency of CR dye adsorption depends on various factors like pH, temperature of the solution, equilibrium time of adsorption, agitation speed, initial concentration of dye and adsorbent dosage. It has been observed that the nanocomposite is having excellent CR dye adsorption capacity (Q0=209.205 mg g(-1)), which is considerably high. The dye adsorption process is controlled by pseudo-second order and intraparticle diffusion kinetic models. The adsorption equilibrium data correlates well with Langmuir isotherm. Desorption study indicates the efficient regeneration ability of the dye loaded nanocomposite. Copyright © 2013 Elsevier Ltd. All rights reserved.

Characteristics of activated carbon and carbon nanotubes as adsorbents to remove annatto (norbixin) in cheese whey.

PubMed

Zhang, Yue; Pan, Kang; Zhong, Qixin

2013-09-25

Removing annatto from cheese whey without bleaching has potential to improve whey protein quality. In this work, the potential of two activated carbon products and multiwalled carbon nanotubes (CNT) was studied for extracting annatto (norbixin) in aqueous solutions. Batch adsorption experiments were studied for the effects of solution pH, adsorbent mass, contact duration, and ionic strength. The equilibrium adsorption data were observed to fit both Langmuir and Freundlich isotherm models. The thermodynamic parameters estimated from adsorption isotherms demonstrated that the adsorption of norbixin on three adsorbents is exothermic, and the entropic contribution differs with adsorbent structure. The adsorption kinetics, with CNT showing a higher rate than activated carbon, followed the pseudo first order and second order rate expressions and demonstrated the significance of intraparticle diffusion. Electrostatic interactions were observed to be significant in the adsorption. The established adsorption parameters may be used in the dairy industry to decolorize cheese whey without applying bleaching agents.

Kinetics and equilibrium models for the sorption of tributyltin to nZnO, activated carbon and nZnO/activated carbon composite in artificial seawater.

PubMed

Ayanda, Olushola S; Fatoki, Olalekan S; Adekola, Folahan A; Ximba, Bhekumusa J

2013-07-15

The removal of tributyltin (TBT) from artificial seawater using nZnO, activated carbon and nZnO/activated carbon composite was systematically studied. The equilibrium and kinetics of adsorption were investigated in a batch adsorption system. Equilibrium adsorption data were analyzed using Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (D-R) isotherm models. Pseudo first- and second-order, Elovich, fractional power and intraparticle diffusion models were applied to test the kinetic data. Thermodynamic parameters such as ΔG°, ΔS° and ΔH° were also calculated to understand the mechanisms of adsorption. Optimal conditions for the adsorption of TBT from artificial seawater were then applied to TBT removal from natural seawater. A higher removal efficiency of TBT (>99%) was obtained for the nZnO/activated carbon composite material and for activated carbon but not for nZnO. Copyright © 2013 Elsevier Ltd. All rights reserved.

Pecan nutshell as biosorbent to remove Cu(II), Mn(II) and Pb(II) from aqueous solutions.

PubMed

Vaghetti, Julio C P; Lima, Eder C; Royer, Betina; da Cunha, Bruna M; Cardoso, Natali F; Brasil, Jorge L; Dias, Silvio L P

2009-02-15

In the present study we reported for the first time the feasibility of pecan nutshell (PNS, Carya illinoensis) as an alternative biosorbent to remove Cu(II), Mn(II) and Pb(II) metallic ions from aqueous solutions. The ability of PNS to remove the metallic ions was investigated by using batch biosorption procedure. The effects such as, pH, biosorbent dosage on the adsorption capacities of PNS were studied. Four kinetic models were tested, being the adsorption kinetics better fitted to fractionary-order kinetic model. Besides that, the kinetic data were also fitted to intra-particle diffusion model, presenting three linear regions, indicating that the kinetics of adsorption should follow multiple sorption rates. The equilibrium data were fitted to Langmuir, Freundlich, Sips and Redlich-Peterson isotherm models. Taking into account a statistical error function, the data were best fitted to Sips isotherm model. The maximum biosorption capacities of PNS were 1.35, 1.78 and 0.946mmolg(-1) for Cu(II), Mn(II) and Pb(II), respectively.

Characterization of biochars derived from agriculture wastes and their adsorptive removal of atrazine from aqueous solution: A comparative study.

PubMed

Liu, Na; Charrua, Alberto Bento; Weng, Chih-Huang; Yuan, Xiaoling; Ding, Feng

2015-12-01

The physicochemical properties of biochars produced from soybeans (SBB), corn stalks (CSB), rice stalks (RSB), poultry manure (PMB), cattle manure (CMB), and pig manure (PgMB) and their adsorption characteristics of atrazine were investigated. The adsorption capacity increased with the increase of temperature and initial atrazine concentration. More atrazine was removed from basic solutions than acidic solutions, due to the effects of adsorption and hydrolysis. The Freundlich isotherm adsorption parameters indicated that the adsorption capacity decreased in the order SBB>RSB>CMB>CSB>PMB>PgMB, which is associated to the pore volume of biochars. The total pore volume and biochar pH were concluded to play important roles in determining the adsorption capacity, and they may have contributed to physical adsorption mechanisms dominating the overall adsorption process (the low activation energy for all of the biochars). Modified Freundlich and intraparticle diffusion models were used to describe the kinetics of the adsorption process. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adsorption of cadmium(II) on waste biomaterial.

PubMed

Baláž, M; Bujňáková, Z; Baláž, P; Zorkovská, A; Danková, Z; Briančin, J

2015-09-15

Significant increase of the adsorption ability of the eggshell biomaterial toward cadmium was observed upon milling, as is evidenced by the value of maximum monolayer adsorption capacity of 329mgg(-1), which is markedly higher than in the case of most "green" sorbents. The main driving force of the adsorption was proven to be the presence of aragonite phase as a consequence of phase transformation from calcite occurring during milling. Cadmium is adsorbed in a non-reversible way, as documented by different techniques (desorption tests, XRD and EDX measurements). The optimum pH for cadmium adsorption was 7. The adsorption process was accompanied by the increase of the value of specific surface area. The course of adsorption has been described by Langmuir, Freundlich and Dubinin-Radushkevich isotherms. The adsorption kinetics was evaluated using three models, among which the best correlation coefficients and the best normalized standard deviation values were achieved for the pseudo-second order model and the intraparticle diffusion model, respectively. Copyright © 2015 Elsevier Inc. All rights reserved.

Equilibrium and Kinetic Studies of Cd2+ Biosorption by the Brown Algae Sargassum fusiforme

PubMed Central

Zou, Hui-Xi; Li, Nan; Wang, Li-Hua; Yu, Ping; Yan, Xiu-Feng

2014-01-01

A fundamental investigation of the biosorption of Cd2+ from aqueous solution by the edible seaweed Sargassum fusiforme was performed under batch conditions. The influences of experimental parameters, such as the initial pH, sorption time, temperature, and initial Cd2+ concentration, on Cd2+ uptake by S. fusiforme were evaluated. The results indicated that the biosorption of Cd2+ depended on the initial Cd2+ concentration, as well as the pH. The uptake of Cd2+ could be described by the Langmuir isotherm model, and both the Langmuir biosorption equilibrium constant and the maximum biosorption capacity of the monolayer decreased with increasing temperature, thereby confirming the exothermic character of the sorption process. The biosorption kinetics follows the pseudo-second-order kinetic model, and intraparticle diffusion is the sole rate-limiting step for the entire biosorption period. These fundamental equilibrium and kinetic results can support further studies to the removal of cadmium from S. fusiforme harvested from cadmium-polluted waters. PMID:24736449

PNIPAm grafted amino-functionalized mesoporous silica for thermo-responsive chromium elimination

NASA Astrophysics Data System (ADS)

Chang, Jeong Ho; Kim, Jinwon; Lee, Hyesun

2017-12-01

In this study, the effective elimination of Cr(VI) was achieved by thermo-responsive polymer-grafted amino-functionalized mesoporous silica (MS@APTES@PNIPAm) in aqueous solution. The MS@APTES@PNIPAm was successfully synthesized by the coupling of 3-MOP and N-isopropyl acrylamide (NIPAm) in 3-aminoproyltriethoxysilane (APTES) grafted mesoporous silica surface. The thermo-responsive elimination of Cr(VI) was demonstrated at various pH levels and at room temperature and 40 °C, respectively. The characterization of the synthesized materials was achieved by scanning electron microscopy (SEM), thermogravimetric analysis (TGA), Fourier transform infrared spectroscopy (FT-IR) and nitrogen (N2) adsorption-desorption. The maximum adsorption of hexavalent chromium on MS@APTES@PNIPAm in aqueous solution was 123.8 mg g-1 at 40 °C in pH 2.5. Furthermore, the results of isotherm and kinetic experiments demonstrated that the adsorption behavior of Cr(VI) on MS@APTES@PNIPAm was well fitted to a Langmuir plot with a pseudo-second-order and intra-particle diffusion model.

Mass-transfer limitations for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor.

PubMed

Xiu, G H; Jiang, L; Li, P

2001-07-05

A mathematical model has been developed for immobilized enzyme-catalyzed kinetic resolution of racemate in a fixed-bed reactor in which the enzyme-catalyzed reaction (the irreversible uni-uni competitive Michaelis-Menten kinetics is chosen as an example) was coupled with intraparticle diffusion, external mass transfer, and axial dispersion. The effects of mass-transfer limitations, competitive inhibition of substrates, deactivation on the enzyme effective enantioselectivity, and the optical purity and yield of the desired product are examined quantitatively over a wide range of parameters using the orthogonal collocation method. For a first-order reaction, an analytical solution is derived from the mathematical model for slab-, cylindrical-, and spherical-enzyme supports. Based on the analytical solution for the steady-state resolution process, a new concise formulation is presented to predict quantitatively the mass-transfer limitations on enzyme effective enantioselectivity and optical purity and yield of the desired product for a continuous steady-state kinetic resolution process in a fixed-bed reactor. Copyright 2001 John Wiley & Sons, Inc.

Removal of lead from aqueous solutions with a treated spent bleaching earth.

PubMed

Mana, Mohamed; Ouali, Mohand Said; Lindheimer, Marc; Menorval, Louis Charles de

2008-11-30

A spent bleaching earth from an edible oil refinery has been treated by impregnation with a normal sodium hydroxide solution followed by mild thermal treatment (100 degrees C). The obtained material (TSBE) was washed, dried and characterized by X-ray diffraction, FTIR, SEM, BET and thermal analysis. The clay structure was not apparently affected by the treatment and the impregnated organic matter was quantitatively removed. We have investigated the sorption of lead on this material, the spent bleaching earth (SBE) and the virgin bleaching earth (VBE). The kinetic results fit the pseudo second-order kinetic model and the Weber & Morris, intraparticle diffusion model. The pH had effect on the sorption efficiency. The sorption isotherms followed the Langmuir model for various sorbent concentrations with good values of determination coefficient. A comparison between the results obtained with this material and those of the literature highlighted a good removal capacity of the treated spent bleaching earth at low cost.

Strongly anomalous diffusion in sheared magnetic configurations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vanden Eijnden, E.; Balescu, R.

1996-03-01

The statistical behavior of magnetic lines in a sheared magnetic configuration with reference surface {ital x}=0 is investigated within the framework of the kinetic theory. A Liouville equation is associated with the equations of motion of the stochastic magnetic lines. After averaging over an ensemble of realizations, it yields a convection-diffusion equation within the quasilinear approximation. The diffusion coefficients are space dependent and peaked around the reference surface {ital x}=0. Due to the shear, the diffusion of lines away from the reference surface is slowed down. The behavior of the lines is asymptotically strongly non-Gaussian. The reference surface acts likemore » an attractor around which the magnetic lines spread with an effective subdiffusive behavior. Comparison is also made with more usual treatments based on the study of the first two moments equations. For sheared systems, it is explicitly shown that the Corrsin approximation assumed in the latter approach is no longer valid. It is also concluded that the diffusion coefficients cannot be derived from the mean square displacement of the magnetic lines in an inhomogeneous medium. {copyright} {ital 1996 American Institute of Physics.}« less

Continuum mesoscopic framework for multiple interacting species and processes on multiple site types and/or crystallographic planes.

PubMed

Chatterjee, Abhijit; Vlachos, Dionisios G

2007-07-21

While recently derived continuum mesoscopic equations successfully bridge the gap between microscopic and macroscopic physics, so far they have been derived only for simple lattice models. In this paper, general deterministic continuum mesoscopic equations are derived rigorously via nonequilibrium statistical mechanics to account for multiple interacting surface species and multiple processes on multiple site types and/or different crystallographic planes. Adsorption, desorption, reaction, and surface diffusion are modeled. It is demonstrated that contrary to conventional phenomenological continuum models, microscopic physics, such as the interaction potential, determines the final form of the mesoscopic equation. Models of single component diffusion and binary diffusion of interacting particles on single-type site lattice and of single component diffusion on complex microporous materials' lattices consisting of two types of sites are derived, as illustrations of the mesoscopic framework. Simplification of the diffusion mesoscopic model illustrates the relation to phenomenological models, such as the Fickian and Maxwell-Stefan transport models. It is demonstrated that the mesoscopic equations are in good agreement with lattice kinetic Monte Carlo simulations for several prototype examples studied.

Finite Difference Formulation for Prediction of Water Pollution

NASA Astrophysics Data System (ADS)

Johari, Hanani; Rusli, Nursalasawati; Yahya, Zainab

2018-03-01

Water is an important component of the earth. Human being and living organisms are demand for the quality of water. Human activity is one of the causes of the water pollution. The pollution happened give bad effect to the physical and characteristic of water contents. It is not practical to monitor all aspects of water flow and transport distribution. So, in order to help people to access to the polluted area, a prediction of water pollution concentration must be modelled. This study proposed a one-dimensional advection diffusion equation for predicting the water pollution concentration transport. The numerical modelling will be produced in order to predict the transportation of water pollution concentration. In order to approximate the advection diffusion equation, the implicit Crank Nicolson is used. For the purpose of the simulation, the boundary condition and initial condition, the spatial steps and time steps as well as the approximations of the advection diffusion equation have been encoded. The results of one dimensional advection diffusion equation have successfully been used to predict the transportation of water pollution concentration by manipulating the velocity and diffusion parameters.

Mathematical analysis of thermal diffusion shock waves

NASA Astrophysics Data System (ADS)

Gusev, Vitalyi; Craig, Walter; Livoti, Roberto; Danworaphong, Sorasak; Diebold, Gerald J.

2005-10-01

Thermal diffusion, also known as the Ludwig-Soret effect, refers to the separation of mixtures in a temperature gradient. For a binary mixture the time dependence of the change in concentration of each species is governed by a nonlinear partial differential equation in space and time. Here, an exact solution of the Ludwig-Soret equation without mass diffusion for a sinusoidal temperature field is given. The solution shows that counterpropagating shock waves are produced which slow and eventually come to a halt. Expressions are found for the shock time for two limiting values of the starting density fraction. The effects of diffusion on the development of the concentration profile in time and space are found by numerical integration of the nonlinear differential equation.

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

NASA Astrophysics Data System (ADS)

Remizov, I. D.

2012-07-01

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.

Modeling boundary measurements of scattered light using the corrected diffusion approximation

PubMed Central

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, Arnold D.

2012-01-01

We study the modeling and simulation of steady-state measurements of light scattered by a turbid medium taken at the boundary. In particular, we implement the recently introduced corrected diffusion approximation in two spatial dimensions to model these boundary measurements. This implementation uses expansions in plane wave solutions to compute boundary conditions and the additive boundary layer correction, and a finite element method to solve the diffusion equation. We show that this corrected diffusion approximation models boundary measurements substantially better than the standard diffusion approximation in comparison to numerical solutions of the radiative transport equation. PMID:22435102

Optical Oversampled Analog-to-Digital Conversion

DTIC Science & Technology

1992-06-29

hologram weights and interconnects in the digital image halftoning configuration. First, no temporal error diffusion occurs in the digital image... halftoning error diffusion ar- chitecture as demonstrated by Equation (6.1). Equation (6.2) ensures that the hologram weights sum to one so that the exact...optimum halftone image should be faster. Similarly, decreased convergence time suggests that an error diffusion filter with larger spatial dimensions

Modelling the radiotherapy effect in the reaction-diffusion equation.

PubMed

Borasi, Giovanni; Nahum, Alan

2016-09-01

In recent years, the reaction-diffusion (Fisher-Kolmogorov) equation has received much attention from the oncology research community due to its ability to describe the infiltrating nature of glioblastoma multiforme and its extraordinary resistance to any type of therapy. However, in a number of previous papers in the literature on applications of this equation, the term (R) expressing the 'External Radiotherapy effect' was incorrectly derived. In this note we derive an analytical expression for this term in the correct form to be included in the reaction-diffusion equation. The R term has been derived starting from the Linear-Quadratic theory of cell killing by ionizing radiation. The correct definition of R was adopted and the basic principles of differential calculus applied. The compatibility of the R term derived here with the reaction-diffusion equation was demonstrated. Referring to a typical glioblastoma tumour, we have compared the results obtained using our expression for the R term with the 'incorrect' expression proposed by other authors. Copyright © 2016 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION.

PubMed

Liu, F; Meerschaert, M M; McGough, R J; Zhuang, P; Liu, Q

2013-03-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

NUMERICAL METHODS FOR SOLVING THE MULTI-TERM TIME-FRACTIONAL WAVE-DIFFUSION EQUATION

PubMed Central

Liu, F.; Meerschaert, M.M.; McGough, R.J.; Zhuang, P.; Liu, Q.

2013-01-01

In this paper, the multi-term time-fractional wave-diffusion equations are considered. The multi-term time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian. PMID:23772179

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Traveling wave solutions to a reaction-diffusion equation

NASA Astrophysics Data System (ADS)

Feng, Zhaosheng; Zheng, Shenzhou; Gao, David Y.

2009-07-01

In this paper, we restrict our attention to traveling wave solutions of a reaction-diffusion equation. Firstly we apply the Divisor Theorem for two variables in the complex domain, which is based on the ring theory of commutative algebra, to find a quasi-polynomial first integral of an explicit form to an equivalent autonomous system. Then through this first integral, we reduce the reaction-diffusion equation to a first-order integrable ordinary differential equation, and a class of traveling wave solutions is obtained accordingly. Comparisons with the existing results in the literature are also provided, which indicates that some analytical results in the literature contain errors. We clarify the errors and instead give a refined result in a simple and straightforward manner.

Nature of self-diffusion in two-dimensional fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Nature of self-diffusion in two-dimensional fluids

DOE PAGES

Choi, Bongsik; Han, Kyeong Hwan; Kim, Changho; ...

2017-12-18

Self-diffusion in a two-dimensional simple fluid is investigated by both analytical and numerical means. We investigate the anomalous aspects of self-diffusion in two-dimensional fluids with regards to the mean square displacement, the time-dependent diffusion coefficient, and the velocity autocorrelation function (VACF) using a consistency equation relating these quantities. Here, we numerically confirm the consistency equation by extensive molecular dynamics simulations for finite systems, corroborate earlier results indicating that the kinematic viscosity approaches a finite, non-vanishing value in the thermodynamic limit, and establish the finite size behavior of the diffusion coefficient. We obtain the exact solution of the consistency equation in the thermodynamic limit and use this solution to determine the large time asymptotics of the mean square displacement, the diffusion coefficient, and the VACF. An asymptotic decay law of the VACF resembles the previously known self-consistent form, 1/(more » $$t\\sqrt{In t)}$$ however with a rescaled time.« less

Perturbed invariant subspaces and approximate generalized functional variable separation solution for nonlinear diffusion-convection equations with weak source

NASA Astrophysics Data System (ADS)

Xia, Ya-Rong; Zhang, Shun-Li; Xin, Xiang-Peng

2018-03-01

In this paper, we propose the concept of the perturbed invariant subspaces (PISs), and study the approximate generalized functional variable separation solution for the nonlinear diffusion-convection equation with weak source by the approximate generalized conditional symmetries (AGCSs) related to the PISs. Complete classification of the perturbed equations which admit the approximate generalized functional separable solutions (AGFSSs) is obtained. As a consequence, some AGFSSs to the resulting equations are explicitly constructed by way of examples.

Diffuse reflectance relations based on diffusion dipole theory for large absorption and reduced scattering

NASA Astrophysics Data System (ADS)

Bremmer, Rolf H.; van Gemert, Martin J. C.; Faber, Dirk J.; van Leeuwen, Ton G.; Aalders, Maurice C. G.

2013-08-01

Diffuse reflectance spectra are used to determine the optical properties of biological samples. In medicine and forensic science, the turbid objects under study often possess large absorption and/or scattering properties. However, data analysis is frequently based on the diffusion approximation to the radiative transfer equation, implying that it is limited to tissues where the reduced scattering coefficient dominates over the absorption coefficient. Nevertheless, up to absorption coefficients of 20 m at reduced scattering coefficients of 1 and 11.5 mm-1, we observed excellent agreement (r2=0.994) between reflectance measurements of phantoms and the diffuse reflectance equation proposed by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], derived as an approximation to one of the diffusion dipole equations of Farrell et al. [Med. Phys. 19, 879-888 (1992)]. However, two parameters were fitted to all phantom experiments, including strongly absorbing samples, implying that the reflectance equation differs from diffusion theory. Yet, the exact diffusion dipole approximation at high reduced scattering and absorption also showed agreement with the phantom measurements. The mathematical structure of the diffuse reflectance relation used, derived by Zonios et al. [Appl. Opt. 38, 6628-6637 (1999)], explains this observation. In conclusion, diffuse reflectance relations derived as an approximation to the diffusion dipole theory of Farrell et al. can analyze reflectance ratios accurately, even for much larger absorption than reduced scattering coefficients. This allows calibration of fiber-probe set-ups so that the object's diffuse reflectance can be related to its absorption even when large. These findings will greatly expand the application of diffuse reflection spectroscopy. In medicine, it may allow the use of blue/green wavelengths and measurements on whole blood, and in forensic science, it may allow inclusion of objects such as blood stains and cloth at crime scenes.

Diffusion in random networks: Asymptotic properties, and numerical and engineering approximations

NASA Astrophysics Data System (ADS)

Padrino, Juan C.; Zhang, Duan Z.

2016-11-01

The ensemble phase averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of a set of pockets connected by tortuous channels. Inside a channel, we assume that fluid transport is governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pores mass density. The so-called dual porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain, whose solution is sought numerically. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt- 1 / 4 rather than xt- 1 / 2 as in the traditional theory. This early time sub-diffusive similarity can be explained by random walk theory through the network. In addition, by applying concepts of fractional calculus, we show that, for small time, the governing equation reduces to a fractional diffusion equation with known solution. We recast this solution in terms of special functions easier to compute. Comparison of the numerical and exact solutions shows excellent agreement.

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Is the kinetic equation for turbulent gas-particle flows ill posed?

PubMed

Reeks, M; Swailes, D C; Bragg, A D

2018-02-01

This paper is about the kinetic equation for gas-particle flows, in particular its well-posedness and realizability and its relationship to the generalized Langevin model (GLM) probability density function (PDF) equation. Previous analyses, e.g. [J.-P. Minier and C. Profeta, Phys. Rev. E 92, 053020 (2015)PLEEE81539-375510.1103/PhysRevE.92.053020], have concluded that this kinetic equation is ill posed, that in particular it has the properties of a backward heat equation, and as a consequence, its solution will in the course of time exhibit finite-time singularities. We show that this conclusion is fundamentally flawed because it ignores the coupling between the phase space variables in the kinetic equation and the time and particle inertia dependence of the phase space diffusion tensor. This contributes an extra positive diffusion that always outweighs the negative diffusion associated with the dispersion along one of the principal axes of the phase space diffusion tensor. This is confirmed by a numerical evaluation of analytic solutions of these positive and negative contributions to the particle diffusion coefficient along this principal axis. We also examine other erroneous claims and assumptions made in previous studies that demonstrate the apparent superiority of the GLM PDF approach over the kinetic approach. In so doing, we have drawn attention to the limitations of the GLM approach, which these studies have ignored or not properly considered, to give a more balanced appraisal of the benefits of both PDF approaches.

Optimally designed gold nanorattles with strong built-in hotspots and weak polarization dependence

NASA Astrophysics Data System (ADS)

Zhang, Xuemin; Wang, Tieqiang; Li, Yunong; Fu, Yu; Guo, Lei

2017-12-01

Localized electromagnetic fields generated by interparticle plasmon coupling suffer greatly from nonreproducibility because they are extremely sensitive to the nanoparticle aggregation status and the incident polarization. Here, we synthesize gold nanorattles that exhibit inherent aggregation-insensitive hotspots due to the intraparticle core-shell plasmon coupling, and investigate the structural effect on the intraparticle coupling strength and its polarization dependence. Through optimizing the structural parameters, we successfully synthesize gold nanorattles with strong built-in hotspots and weak polarization dependence. These aggregation-insensitive and weakly polarization-dependent hotspots make the Raman enhancement from nanorattle aggregates show an unusual weak dependence on the particle aggregation status, which therefore affords the opportunity to fabricate uniform and reproducible surface enhanced Raman scattering substrates.

Void Formation during Diffusion - Two-Dimensional Approach

NASA Astrophysics Data System (ADS)

Wierzba, Bartek

2016-06-01

The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst-Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

New Solution of Diffusion-Advection Equation for Cosmic-Ray Transport Using Ultradistributions

NASA Astrophysics Data System (ADS)

Rocca, M. C.; Plastino, A. R.; Plastino, A.; Ferri, G. L.; de Paoli, A.

2015-11-01

In this paper we exactly solve the diffusion-advection equation (DAE) for cosmic-ray transport. For such a purpose we use the Theory of Ultradistributions of J. Sebastiao e Silva, to give a general solution for the DAE. From the ensuing solution, we obtain several approximations as limiting cases of various situations of physical and astrophysical interest. One of them involves Solar cosmic-rays' diffusion.

A Least-Squares Transport Equation Compatible with Voids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hansen, Jon; Peterson, Jacob; Morel, Jim

Standard second-order self-adjoint forms of the transport equation, such as the even-parity, odd-parity, and self-adjoint angular flux equation, cannot be used in voids. Perhaps more important, they experience numerical convergence difficulties in near-voids. Here we present a new form of a second-order self-adjoint transport equation that has an advantage relative to standard forms in that it can be used in voids or near-voids. Our equation is closely related to the standard least-squares form of the transport equation with both equations being applicable in a void and having a nonconservative analytic form. However, unlike the standard least-squares form of the transportmore » equation, our least-squares equation is compatible with source iteration. It has been found that the standard least-squares form of the transport equation with a linear-continuous finite-element spatial discretization has difficulty in the thick diffusion limit. Here we extensively test the 1D slab-geometry version of our scheme with respect to void solutions, spatial convergence rate, and the intermediate and thick diffusion limits. We also define an effective diffusion synthetic acceleration scheme for our discretization. Our conclusion is that our least-squares S n formulation represents an excellent alternative to existing second-order S n transport formulations« less

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

A new nonlinear diffusion formalism in a magnetized plasma - Application to space physics and astrophysics

NASA Technical Reports Server (NTRS)

Karimbadi, H.; Krauss-Varban, D.

1992-01-01

A novel diffusion formalism that takes into account the finite width of resonances is presented. The resonance diagram technique is shown to reproduce the details of the particle orbits very accurately, and can be used to determine the acceleration/scattering in the presence of a given wave spectrum. Ways in which the nonlinear orbits can be incorporated into the diffusion equation are shown. The resulting diffusion equation is an extension of the Q-L theory to cases where the waves have large amplitudes and/or are coherent. This new equation does not have a gap at 90 deg in cases where the individual orbits can cross the gap. The conditions under which the resonance gap at 90-deg pitch angle exits are also examined.

Finite-volume scheme for anisotropic diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Solutions for the diurnally forced advection-diffusion equation to estimate bulk fluid velocity and diffusivity in streambeds from temperature time series

NASA Astrophysics Data System (ADS)

Luce, C.; Tonina, D.; Gariglio, F. P.; Applebee, R.

2012-12-01

Differences in the diurnal variations of temperature at different depths in streambed sediments are commonly used for estimating vertical fluxes of water in the streambed. We applied spatial and temporal rescaling of the advection-diffusion equation to derive two new relationships that greatly extend the kinds of information that can be derived from streambed temperature measurements. The first equation provides a direct estimate of the Peclet number from the amplitude decay and phase delay information. The analytical equation is explicit (e.g. no numerical root-finding is necessary), and invertable. The thermal front velocity can be estimated from the Peclet number when the thermal diffusivity is known. The second equation allows for an independent estimate of the thermal diffusivity directly from the amplitude decay and phase delay information. Several improvements are available with the new information. The first equation uses a ratio of the amplitude decay and phase delay information; thus Peclet number calculations are independent of depth. The explicit form also makes it somewhat faster and easier to calculate estimates from a large number of sensors or multiple positions along one sensor. Where current practice requires a priori estimation of streambed thermal diffusivity, the new approach allows an independent calculation, improving precision of estimates. Furthermore, when many measurements are made over space and time, expectations of the spatial correlation and temporal invariance of thermal diffusivity are valuable for validation of measurements. Finally, the closed-form explicit solution allows for direct calculation of propagation of uncertainties in error measurements and parameter estimates, providing insight about error expectations for sensors placed at different depths in different environments as a function of surface temperature variation amplitudes. The improvements are expected to increase the utility of temperature measurement methods for studying groundwater-surface water interactions across space and time scales. We discuss the theoretical implications of the new solutions supported by examples with data for illustration and validation.

The dynamics of oceanic fronts. I - The Gulf Stream

NASA Technical Reports Server (NTRS)

Kao, T. W.

1980-01-01

The establishment and maintenance of the mean hydrographic properties of large-scale density fronts in the upper ocean is considered. The dynamics is studied by posing an initial value problem starting with a near-surface discharge of buoyant water with a prescribed density deficit into an ambient stationary fluid of uniform density; full time dependent diffusion and Navier-Stokes equations are then used with constant eddy diffusion and viscosity coefficients, together with a constant Coriolis parameter. Scaling analysis reveals three independent scales of the problem including the radius of deformation of the inertial length, buoyancy length, and diffusive length scales. The governing equations are then suitably scaled and the resulting normalized equations are shown to depend on the Ekman number alone for problems of oceanic interest. It is concluded that the mean Gulf Stream dynamics can be interpreted in terms of a solution of the Navier-Stokes and diffusion equations, with the cross-stream circulation responsible for the maintenance of the front; this mechanism is suggested for the maintenance of the Gulf Stream dynamics.

Research and Development of Methods for Estimating Physicochemical Properties of Organic Compounds of Environmental Concern

DTIC Science & Technology

1979-02-01

coefficient (at equilibrium) when hysteresis is apparent. 6. Coefficient n in Freundlich equation for 1/n soil or sediment adsorption isotherms ýX - KC . 7...Biodegradation Chemical structures cal clasaes (e.g., Diffusion Correlations phenols). General Diffusion coefficients Equations terms for organic...OF THE FATE AND TRANSPORT OF ORGANIC CHEMICALS Adsorption coefficients: K, n* from Freundlich equation + Desorption coefficients: K’*, n’* from

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations.

PubMed

Sánchez-Garduño, Faustino; Pérez-Velázquez, Judith

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D (0) = 0) and advection-degenerate (at h '(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h ( u ): (1)   h '( u ) is constant k , (2)   h '( u ) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE.

Reactive-Diffusive-Advective Traveling Waves in a Family of Degenerate Nonlinear Equations

PubMed Central

Sánchez-Garduño, Faustino

2016-01-01

This paper deals with the analysis of existence of traveling wave solutions (TWS) for a diffusion-degenerate (at D(0) = 0) and advection-degenerate (at h′(0) = 0) reaction-diffusion-advection (RDA) equation. Diffusion is a strictly increasing function and the reaction term generalizes the kinetic part of the Fisher-KPP equation. We consider different forms of the convection term h(u): (1)  h′(u) is constant k, (2)  h′(u) = ku with k > 0, and (3) it is a quite general form which guarantees the degeneracy in the advective term. In Case 1, we prove that the task can be reduced to that for the corresponding equation, where k = 0, and then previous results reported from the authors can be extended. For the other two cases, we use both analytical and numerical tools. The analysis we carried out is based on the restatement of searching TWS for the full RDA equation into a two-dimensional dynamical problem. This consists of searching for the conditions on the parameter values for which there exist heteroclinic trajectories of the ordinary differential equations (ODE) system in the traveling wave coordinates. Throughout the paper we obtain the dynamics by using tools coming from qualitative theory of ODE. PMID:27689131

Nonlocal electrical diffusion equation

NASA Astrophysics Data System (ADS)

Gómez-Aguilar, J. F.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H.; Benavides-Cruz, M.; Calderón-Ramón, C.

2016-07-01

In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is 0<β≤1 and for the time domain is 0<γ≤2. We present solutions for the full fractional equation involving space and time fractional derivatives using numerical methods based on Fourier variable separation. The case with spatial fractional derivatives leads to Levy flight type phenomena, while the time fractional equation is related to sub- or super diffusion. We show that the mathematical concept of fractional derivatives can be useful to understand the behavior of semiconductors, the design of solar panels, electrochemical phenomena and the description of anomalous complex processes.

Numerical analysis for the fractional diffusion and fractional Buckmaster equation by the two-step Laplace Adam-Bashforth method

NASA Astrophysics Data System (ADS)

Jain, Sonal

2018-01-01

In this paper, we aim to use the alternative numerical scheme given by Gnitchogna and Atangana for solving partial differential equations with integer and non-integer differential operators. We applied this method to fractional diffusion model and fractional Buckmaster models with non-local fading memory. The method yields a powerful numerical algorithm for fractional order derivative to implement. Also we present in detail the stability analysis of the numerical method for solving the diffusion equation. This proof shows that this method is very stable and also converges very quickly to exact solution and finally some numerical simulation is presented.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

PubMed

Biswas, Samir Kumar; Kanhirodan, Rajan; Vasu, Ram Mohan; Roy, Debasish

2011-08-01

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

The diffusion approximation. An application to radiative transfer in clouds

NASA Technical Reports Server (NTRS)

Arduini, R. F.; Barkstrom, B. R.

1976-01-01

It is shown how the radiative transfer equation reduces to the diffusion equation. To keep the mathematics as simple as possible, the approximation is applied to a cylindrical cloud of radius R and height h. The diffusion equation separates in cylindrical coordinates and, in a sample calculation, the solution is evaluated for a range of cloud radii with cloud heights of 0.5 km and 1.0 km. The simplicity of the method and the speed with which solutions are obtained give it potential as a tool with which to study the effects of finite-sized clouds on the albedo of the earth-atmosphere system.

On Entropy Production in the Madelung Fluid and the Role of Bohm's Potential in Classical Diffusion

NASA Astrophysics Data System (ADS)

Heifetz, Eyal; Tsekov, Roumen; Cohen, Eliahu; Nussinov, Zohar

2016-07-01

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the "force" accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum.

Building 1D resonance broadened quasilinear (RBQ) code for fast ions Alfvénic relaxations

NASA Astrophysics Data System (ADS)

Gorelenkov, Nikolai; Duarte, Vinicius; Berk, Herbert

2016-10-01

The performance of the burning plasma is limited by the confinement of superalfvenic fusion products, e.g. alpha particles, which are capable of resonating with the Alfvénic eigenmodes (AEs). The effect of AEs on fast ions is evaluated using a resonance line broadened diffusion coefficient. The interaction of fast ions and AEs is captured for cases where there are either isolated or overlapping modes. A new code RBQ1D is being built which constructs diffusion coefficients based on realistic eigenfunctions that are determined by the ideal MHD code NOVA. The wave particle interaction can be reduced to one-dimensional dynamics where for the Alfvénic modes typically the particle kinetic energy is nearly constant. Hence to a good approximation the Quasi-Linear (QL) diffusion equation only contains derivatives in the angular momentum. The diffusion equation is then one dimensional that is efficiently solved simultaneously for all particles with the equation for the evolution of the wave angular momentum. The evolution of fast ion constants of motion is governed by the QL diffusion equations which are adapted to find the ion distribution function.

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Applicability of the Fokker-Planck equation to the description of diffusion effects on nucleation

NASA Astrophysics Data System (ADS)

Sorokin, M. V.; Dubinko, V. I.; Borodin, V. A.

2017-01-01

The nucleation of islands in a supersaturated solution of surface adatoms is considered taking into account the possibility of diffusion profile formation in the island vicinity. It is shown that the treatment of diffusion-controlled cluster growth in terms of the Fokker-Planck equation is justified only provided certain restrictions are satisfied. First of all, the standard requirement that diffusion profiles of adatoms quickly adjust themselves to the actual island sizes (adiabatic principle) can be realized only for sufficiently high island concentration. The adiabatic principle is essential for the probabilities of adatom attachment to and detachment from island edges to be independent of the adatom diffusion profile establishment kinetics, justifying the island nucleation treatment as the Markovian stochastic process. Second, it is shown that the commonly used definition of the "diffusion" coefficient in the Fokker-Planck equation in terms of adatom attachment and detachment rates is justified only provided the attachment and detachment are statistically independent, which is generally not the case for the diffusion-limited growth of islands. We suggest a particular way to define the attachment and detachment rates that allows us to satisfy this requirement as well. When applied to the problem of surface island nucleation, our treatment predicts the steady-state nucleation barrier, which coincides with the conventional thermodynamic expression, even though no thermodynamic equilibrium is assumed and the adatom diffusion is treated explicitly. The effect of adatom diffusional profiles on the nucleation rate preexponential factor is also discussed. Monte Carlo simulation is employed to analyze the applicability domain of the Fokker-Planck equation and the diffusion effect beyond it. It is demonstrated that a diffusional cloud is slowing down the nucleation process for a given monomer interaction with the nucleus edge.

Phosphorus immobilization in micropores of drinking-water treatment residuals: implications for long-term stability.

PubMed

Makris, Konstantinos C; Harris, Willie G; O'Connor, George A; Obreza, Thomas A

2004-12-15

Drinking-water treatment residuals (WTRs) can immobilize excess soil phosphorus (P), but little is known about the long-term P retention by WTRs. To evaluate the long-term P sorption characteristics of one Fe- and one Al-based WTR, physicochemical properties pertinent to time-dependency and hysteresis of P sorption were assessed. This study also investigated the P sorption mechanisms that could affect the long-term stability of sorbed P by WTRs. Phosphorus sorption kinetics by the WTRs exhibited a slow phase that followed an initial rapid phase, as typically occurs with metal hydroxides. Phosphorus sorption maxima for both Fe- and Al-based WTRs exceeded 9100 mg of P kg(-1) and required a greater specific surface area (SSA) than would be available based on BET-N2 calculations. Electron microprobe analyses of cross-sectional, P-treated particles showed three-dimensional P sorption by WTRs. Carbon dioxide gas sorption was greater than N2, suggesting steric restriction of N2 diffusion by narrow micropore openings. Phosphorus-treated Co2 SSAs were reduced by P treatment, suggesting P sorption by micropores (5-20 A). Mercury intrusion porosimetry indicated negligible macroporosity (pores > 500 A). Slow P sorption kinetics by WTRs may be explained by intraparticle P diffusion in micropores. Micropore-bound P should be stable and immobilized over long periods.

Aqueous sodium borohydride induced thermally stable porous zirconium oxide for quick removal of lead ions

PubMed Central

Nayak, Nadiya B.; Nayak, Bibhuti B.

2016-01-01

Aqueous sodium borohydride (NaBH4) is well known for its reducing property and well-established for the development of metal nanoparticles through reduction method. In contrary, this research paper discloses the importance of aqueous NaBH4 as a precipitating agent towards development of porous zirconium oxide. The boron species present in aqueous NaBH4 play an active role during gelation as well as phase separated out in the form of boron complex during precipitation, which helps to form boron free zirconium hydroxide [Zr(OH)4] in the as-synthesized condition. Evolved in-situ hydrogen (H2) gas-bubbles also play an important role to develop as-synthesized loose zirconium hydroxide and the presence of intra-particle voids in the loose zirconium hydroxide help to develop porous zirconium oxide during calcination process. Without any surface modification, this porous zirconium oxide quickly adsorbs almost hundred percentages of toxic lead ions from water solution within 15 minutes at normal pH condition. Adsorption kinetic models suggest that the adsorption process was surface reaction controlled chemisorption. Quick adsorption was governed by surface diffusion process and the adsorption kinetic was limited by pore diffusion. Five cycles of adsorption-desorption result suggests that the porous zirconium oxide can be reused efficiently for removal of Pb (II) ions from aqueous solution. PMID:26980545

Removal of bisphenol A by adsorption mechanism using PES-SiO2 composite membranes.

PubMed

Muhamad, Mimi Suliza; Salim, Mohd Razman; Lau, Woei Jye; Hadibarata, Tony; Yusop, Zulkifli

2016-08-01

Polyethersulphone (PES) membranes blended with silicon dioxide (SiO2) nanoparticles were prepared via a dry-jet wet spinning technique for the removal of bisphenol A (BPA) by adsorption mechanism. The morphology of SiO2 nanoparticles was analysed using a transmission electron microscopy and particle size distribution was also analysed. The prepared membranes were characterized by several techniques including field emission scanning electron microscopy, Fourier transform infrared spectroscopy and water contact angle. The adsorption mechanism of membrane towards BPA was evaluated by batch experiments and kinetic model. The influence of natural organic matter (NOM) in feed water on membrane BPA removal was also studied by filtration experiments. Results showed that BPA adsorption capacity as high as 53 µg/g could be achieved by the PES membrane incorporated with 2 wt% SiO2 in which the adsorption mechanism was in accordance with the pseudo-second-order kinetic model. The intraparticles diffusion model suggested that the rate limiting factor of membrane adsorption mechanism is governed by the diffusion of BPA into the membrane pores. The presence of 10 ppm NOM has reported to negatively reduce BPA removal by 24%, as it tended to compete with BPA for membrane adsorption. This work has demonstrated that PES-SiO2 membrane has the potential to eliminate trace amount of BPA from water source containing NOM.

Product layer development during sulfation and sulfidation of uncalcined limestone particles at elevated pressures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zevenhoven, C.A.P.; Yrjas, K.P.; Hupa, M.M.

1998-07-01

Fluidized bed combustion or gasification allows for in-bed sulfur capture with a calcium-based sorbent such as limestone or dolomite. Sorbent particle size, porosity, internal surface, and their variation during conversion have great influence on the conversion of the sorbent. The uptake of SO{sub 2} and H{sub 2}S by five physically different limestones is discussed, for typical pressurized fluidized bed combustor or gasifier conditions: 850/950 C, 15/20 bar. Tests were done in a pressurized thermogravimetric apparatus (P-TGA), the size of the limestone particles was 250--300 {micro}m. It is stressed that the limestones remain uncalcined. A changing internal structure (CIS) model ismore » presented in which reaction kinetics and product layer diffusion are related to the intraparticle surface of reaction, instead of the outer particle surface as in unreacted shrinking core (USC)-type models. The random pore model was used for describing the changing internal pore and reaction surfaces. Rate parameters were extracted for all five limestones using the CIS model and a USC model with variable effective diffusivity. Differences in the sulfur capture performance of the limestones were evaluated. Plots of the CaSO{sub 4} or CaS product layer thickness as a function of conversion are given, and the relative importance of limestone porosity and internal surface is discussed.« less

[Adsorption kinetics and mechanism of lead (II) on polyamine-functionalized mesoporous activated carbon].

PubMed

Li, Kun-Quan; Wang, Yan-Jin; Yang, Mei-Rong; Zhu, Zhi-Qiang; Zheng, Zheng

2014-08-01

Bagasse mesoporous carbon was prepared by microwave assisted H3 PO4 activation. Amido and imido groups were modified with ethanediamine on the channels' surface of mesoporous carbon through nitric oxidation and amide reaction. The influence of Pb(II) concentration, adsorption time on Pb(II) adsorption on the ethanediamine-modified mesoporous carbon (AC-EDA) was investigated. The adsorption kinetics and mechanism were also discussed. The results showed that AC-EDA had a great performance for Pb(II) adsorption, and more than 70% of Pb(II) was adsorbed in 5 minutes. The adsorption amount of Pb(II) on the carbon increased with the increase of solution pH in acidic conditions. It was found that AC-EDA had different binding energies on different adsorption sites for Pb(II) separation. The Pb(II) adsorption process on AC-EDA was controlled by intra-particle diffusion in the first 3 min, and then film diffusion played the important pole on the adsorption. The adsorption amount increased with the increase of temperature, indicating the adsorption was an endothermic reaction. The high adsorption energy (> 11 kJ x mol(-1)) implied that the) adsorption was a chemical adsorption. The XPS of AC-EDA before and after Pb(II) adsorption showed that the polyamine group was involved in the adsorption, and should be a main factor of the high efficient adsorption.

Assessment of kinetic models on Fe adsorption in groundwater using high-quality limestone

NASA Astrophysics Data System (ADS)

Akbar, N. A.; Kamil, N. A. F. Mohd; Zin, N. S. Md; Adlan, M. N.; Aziz, H. A.

2018-04-01

During the groundwater pumping process, dissolved Fe2+ is oxidized into Fe3+ and produce rust-coloured iron mineral. Adsorption kinetic models are used to evaluate the performance of limestone adsorbent and describe the mechanism of adsorption and the diffusion processes of Fe adsorption in groundwater. This work presents the best kinetic model of Fe adsorption, which was chosen based on a higher value of coefficient correlation, R2. A batch adsorption experiment was conducted for various contact times ranging from 0 to 135 minutes. From the results of the batch study, three kinetic models were analyzed for Fe removal onto limestone sorbent, including the pseudo-first order (PFO), pseudo-second order (PSO) and intra-particle diffusion (IPD) models. Results show that the adsorption kinetic models follow the sequence: PSO > PFO > IPD, where the values of R2 are 0.997 > 0.919 > 0.918. A high value of R2 (0.997) reveals better fitted experimental data. Furthermore, the value of qe cal in the PSO kinetic model is very near to qe exp rather than that in other models. This finding therefore suggests that the PSO kinetic model has the good fitted with the experimental data which involved chemisorption process of divalent Fe removal in groundwater solution. Thus, limestone adsorbent media found to be an alternative and effective treatment of Fe removal from groundwater.

Diffusion Processes Satisfying a Conservation Law Constraint

DOE PAGES

Bakosi, J.; Ristorcelli, J. R.

2014-03-04

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

Diffusion Processes Satisfying a Conservation Law Constraint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakosi, J.; Ristorcelli, J. R.

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be non-negative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of the allowed sample space. We develop a set of constraints on the drift and diffusion terms of such stochastic models to ensure that both the non-negativity and the unit-sum conservation law constraint are satisfied as the variables evolve in time. We investigate the consequencesmore » of the developed constraints on the Fokker-Planck equation, the associated system of stochastic differential equations, and the evolution equations of the first four moments of the probability density function. We show that random variables, satisfying a conservation law constraint, represented by stochastic diffusion processes, must have diffusion terms that are coupled and nonlinear. The set of constraints developed enables the development of statistical representations of fluctuating variables satisfying a conservation law. We exemplify the results with the bivariate beta process and the multivariate Wright-Fisher, Dirichlet, and Lochner’s generalized Dirichlet processes.« less

A model for shrinkage strain in photo polymerization of dental composites.

PubMed

Petrovic, Ljubomir M; Atanackovic, Teodor M

2008-04-01

We formulate a new model for the shrinkage strain developed during photo polymerization in dental composites. The model is based on the diffusion type fractional order equation, since it has been proved that polymerization reaction is diffusion controlled (Atai M, Watts DC. A new kinetic model for the photo polymerization shrinkage-strain of dental composites and resin-monomers. Dent Mater 2006;22:785-91). Our model strongly confirms the observation by Atai and Watts (see reference details above) and their experimental results. The shrinkage strain is modeled by a nonlinear differential equation in (see reference details above) and that equation must be solved numerically. In our approach, we use the linear fractional order differential equation to describe the strain rate due to photo polymerization. This equation is solved exactly. As shrinkage is a consequence of the polymerization reaction and polymerization reaction is diffusion controlled, we postulate that shrinkage strain rate is described by a diffusion type equation. We find explicit form of solution to this equation and determine the strain in the resin monomers. Also by using equations of linear viscoelasticity, we determine stresses in the polymer due to the shrinkage. The time evolution of stresses implies that the maximal stresses are developed at the very beginning of the polymerization process. The stress in a dental composite that is light treated has the largest value short time after the treatment starts. The strain settles at the constant value in the time of about 100s (for the cases treated in Atai and Watts). From the model developed here, the shrinkage strain of dental composites and resin monomers is analytically determined. The maximal value of stresses is important, since this value must be smaller than the adhesive bond strength at cavo-restoration interface. The maximum stress determined here depends on the diffusivity coefficient. Since diffusivity coefficient increases as polymerization proceeds, it follows that the periods of light treatments should be shorter at the beginning of the treatment and longer at the end of the treatment, with dark interval between the initial low intensity and following high intensity curing. This is because at the end of polymerization the stress relaxation cannot take place.

Isonitrile-functionalized ruthenium nanoparticles: intraparticle charge delocalization through Ru=C=N interfacial bonds

NASA Astrophysics Data System (ADS)

Zhang, Fengqi; Huang, Lin; Zou, Jiasui; Yang, Jun; Kang, Xiongwu; Chen, Shaowei

2017-09-01

Ruthenium nanoparticles (2.06 ± 0.46 nm in diameter) stabilized by 1-hexyl-4-isocyanobenzene (CNBH), denoted as RuCNBH, were prepared by the self-assembly of isonitrile molecules onto the surface of "bare" Ru colloids by virtue of the formation of Ru=C=N- interfacial bonds. FTIR measurements showed that the stretching vibration of the terminal -N≡C bonds at 2119 cm-1 for the monomeric ligands disappeared and concurrently three new bands at 2115, 2043, and 1944 cm-1 emerged with RuCNBH nanoparticles, which was ascribed to the transformation of -N≡C to Ru=C=N- by back donation of Ru-d electrons to the π* orbital of the organic ligands. Metathesis reaction of RuCNBH with vinyl derivatives further corroborated the nature of the Ru=C interfacial bonds. When 1-isocyanopyrene (CNPy) was bounded onto the Ru nanoparticles surface through Ru=C=N interfacial bond (denoted as RuCNPy), the emission maximum was found to red-shift by 27 nm, as compared to that of the CNPy monomers, along with a reduced fluorescence lifetime, due to intraparticle charge delocalization that arose from the conjugated Ru=C=N- interfacial bonds. The results of this study further underline the significance of metal-organic interfacial bonds in the control of intraparticle charge-transfer dynamics and the optical and electronic properties of metal nanoparticles. [Figure not available: see fulltext.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

PubMed

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. Diffusion within the pores is subject to a strict single-file (no passing) constraint. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice-gas model for this reaction-diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction-diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction-diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

Cross-Diffusion Induced Turing Instability and Amplitude Equation for a Toxic-Phytoplankton-Zooplankton Model with Nonmonotonic Functional Response

NASA Astrophysics Data System (ADS)

Han, Renji; Dai, Binxiang

2017-06-01

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored.

Bessel Fourier orientation reconstruction: an analytical EAP reconstruction using multiple shell acquisitions in diffusion MRI.

PubMed

Hosseinbor, Ameer Pasha; Chung, Moo K; Wu, Yu-Chien; Alexander, Andrew L

2011-01-01

The estimation of the ensemble average propagator (EAP) directly from q-space DWI signals is an open problem in diffusion MRI. Diffusion spectrum imaging (DSI) is one common technique to compute the EAP directly from the diffusion signal, but it is burdened by the large sampling required. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed. One, in particular, is Diffusion Propagator Imaging (DPI) which is based on the Laplace's equation estimation of diffusion signal for each shell acquisition. Viewed intuitively in terms of the heat equation, the DPI solution is obtained when the heat distribution between temperatuere measurements at each shell is at steady state. We propose a generalized extension of DPI, Bessel Fourier Orientation Reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition. That is, the heat distribution between shell measurements is no longer at steady state. In addition to being analytical, the BFOR solution also includes an intrinsic exponential smootheing term. We illustrate the effectiveness of the proposed method by showing results on both synthetic and real MR datasets.

Cusping, transport and variance of solutions to generalized Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Carnaffan, Sean; Kawai, Reiichiro

2017-06-01

We study properties of solutions to generalized Fokker-Planck equations through the lens of the probability density functions of anomalous diffusion processes. In particular, we examine solutions in terms of their cusping, travelling wave behaviours, and variance, within the framework of stochastic representations of generalized Fokker-Planck equations. We give our analysis in the cases of anomalous diffusion driven by the inverses of the stable, tempered stable and gamma subordinators, demonstrating the impact of changing the distribution of waiting times in the underlying anomalous diffusion model. We also analyse the cases where the underlying anomalous diffusion contains a Lévy jump component in the parent process, and when a diffusion process is time changed by an uninverted Lévy subordinator. On the whole, we present a combination of four criteria which serve as a theoretical basis for model selection, statistical inference and predictions for physical experiments on anomalously diffusing systems. We discuss possible applications in physical experiments, including, with reference to specific examples, the potential for model misclassification and how combinations of our four criteria may be used to overcome this issue.

Anomalous Transport of Cosmic Rays in a Nonlinear Diffusion Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Litvinenko, Yuri E.; Fichtner, Horst; Walter, Dominik

2017-05-20

We investigate analytically and numerically the transport of cosmic rays following their escape from a shock or another localized acceleration site. Observed cosmic-ray distributions in the vicinity of heliospheric and astrophysical shocks imply that anomalous, superdiffusive transport plays a role in the evolution of the energetic particles. Several authors have quantitatively described the anomalous diffusion scalings, implied by the data, by solutions of a formal transport equation with fractional derivatives. Yet the physical basis of the fractional diffusion model remains uncertain. We explore an alternative model of the cosmic-ray transport: a nonlinear diffusion equation that follows from a self-consistent treatmentmore » of the resonantly interacting cosmic-ray particles and their self-generated turbulence. The nonlinear model naturally leads to superdiffusive scalings. In the presence of convection, the model yields a power-law dependence of the particle density on the distance upstream of the shock. Although the results do not refute the use of a fractional advection–diffusion equation, they indicate a viable alternative to explain the anomalous diffusion scalings of cosmic-ray particles.« less

Some Fundamental Issues of Mathematical Simulation in Biology

NASA Astrophysics Data System (ADS)

Razzhevaikin, V. N.

2018-02-01

Some directions of simulation in biology leading to original formulations of mathematical problems are overviewed. Two of them are discussed in detail: the correct solvability of first-order linear equations with unbounded coefficients and the construction of a reaction-diffusion equation with nonlinear diffusion for a model of genetic wave propagation.

Numerical study of centrifugal compressor stage vaneless diffusers

NASA Astrophysics Data System (ADS)

Galerkin, Y.; Soldatova, K.; Solovieva, O.

2015-08-01

The authors analyzed CFD calculations of flow in vaneless diffusers with relative width in range from 0.014 to 0.100 at inlet flow angles in range from 100 to 450 with different inlet velocity coefficients, Reynolds numbers and surface roughness. The aim is to simulate calculated performances by simple algebraic equations. The friction coefficient that represents head losses as friction losses is proposed for simulation. The friction coefficient and loss coefficient are directly connected by simple equation. The advantage is that friction coefficient changes comparatively little in range of studied parameters. Simple equations for this coefficient are proposed by the authors. The simulation accuracy is sufficient for practical calculations. To create the complete algebraic model of the vaneless diffuser the authors plan to widen this method of modeling to diffusers with different relative length and for wider range of Reynolds numbers.

Integral approximations to classical diffusion and smoothed particle hydrodynamics

DOE PAGES

Du, Qiang; Lehoucq, R. B.; Tartakovsky, A. M.

2014-12-31

The contribution of the paper is the approximation of a classical diffusion operator by an integral equation with a volume constraint. A particular focus is on classical diffusion problems associated with Neumann boundary conditions. By exploiting this approximation, we can also approximate other quantities such as the flux out of a domain. Our analysis of the model equation on the continuum level is closely related to the recent work on nonlocal diffusion and peridynamic mechanics. In particular, we elucidate the role of a volumetric constraint as an approximation to a classical Neumann boundary condition in the presence of physical boundary.more » The volume-constrained integral equation then provides the basis for accurate and robust discretization methods. As a result, an immediate application is to the understanding and improvement of the Smoothed Particle Hydrodynamics (SPH) method.« less

Spin diffusion and torques in disordered antiferromagnets

NASA Astrophysics Data System (ADS)

Manchon, Aurelien

2017-03-01

We have developed a drift-diffusion equation of spin transport in collinear bipartite metallic antiferromagnets. Starting from a model tight-binding Hamiltonian, we obtain the quantum kinetic equation within Keldysh formalism and expand it to the lowest order in spatial gradient using Wigner expansion method. In the diffusive limit, these equations track the spatio-temporal evolution of the spin accumulations and spin currents on each sublattice of the antiferromagnet. We use these equations to address the nature of the spin transfer torque in (i) a spin-valve composed of a ferromagnet and an antiferromagnet, (ii) a metallic bilayer consisting of an antiferromagnet adjacent to a heavy metal possessing spin Hall effect, and in (iii) a single antiferromagnet possessing spin Hall effect. We show that the latter can experience a self-torque thanks to the non-vanishing spin Hall effect in the antiferromagnet.

Breakdown of the reaction-diffusion master equation with nonelementary rates

NASA Astrophysics Data System (ADS)

Smith, Stephen; Grima, Ramon

2016-05-01

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

NASA Astrophysics Data System (ADS)

Broche, Rita de Cássia D. S.; de Oliveira, Luiz Augusto F.

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem.

Fick's second law transformed: one path to cloaking in mass diffusion.

PubMed

Guenneau, S; Puvirajesinghe, T M

2013-06-06

Here, we adapt the concept of transformational thermodynamics, whereby the flux of temperature is controlled via anisotropic heterogeneous diffusivity, for the diffusion and transport of mass concentration. The n-dimensional, time-dependent, anisotropic heterogeneous Fick's equation is considered, which is a parabolic partial differential equation also applicable to heat diffusion, when convection occurs, for example, in fluids. This theory is illustrated with finite-element computations for a liposome particle surrounded by a cylindrical multi-layered cloak in a water-based environment, and for a spherical multi-layered cloak consisting of layers of fluid with an isotropic homogeneous diffusivity, deduced from an effective medium approach. Initial potential applications could be sought in bioengineering.

Stefan-Maxwell Relations and Heat Flux with Anisotropic Transport Coefficients for Ionized Gases in a Magnetic Field with Application to the Problem of Ambipolar Diffusion

NASA Astrophysics Data System (ADS)

Kolesnichenko, A. V.; Marov, M. Ya.

2018-01-01

The defining relations for the thermodynamic diffusion and heat fluxes in a multicomponent, partially ionized gas mixture in an external electromagnetic field have been obtained by the methods of the kinetic theory. Generalized Stefan-Maxwell relations and algebraic equations for anisotropic transport coefficients (the multicomponent diffusion, thermal diffusion, electric and thermoelectric conductivity coefficients as well as the thermal diffusion ratios) associated with diffusion-thermal processes have been derived. The defining second-order equations are derived by the Chapman-Enskog procedure using Sonine polynomial expansions. The modified Stefan-Maxwell relations are used for the description of ambipolar diffusion in the Earth's ionospheric plasma (in the F region) composed of electrons, ions of many species, and neutral particles in a strong electromagnetic field.

From quantum stochastic differential equations to Gisin-Percival state diffusion

NASA Astrophysics Data System (ADS)

Parthasarathy, K. R.; Usha Devi, A. R.

2017-08-01

Starting from the quantum stochastic differential equations of Hudson and Parthasarathy [Commun. Math. Phys. 93, 301 (1984)] and exploiting the Wiener-Itô-Segal isomorphism between the boson Fock reservoir space Γ (L2(R+ ) ⊗(Cn⊕Cn ) ) and the Hilbert space L2(μ ) , where μ is the Wiener probability measure of a complex n-dimensional vector-valued standard Brownian motion {B (t ) ,t ≥0 } , we derive a non-linear stochastic Schrödinger equation describing a classical diffusion of states of a quantum system, driven by the Brownian motion B. Changing this Brownian motion by an appropriate Girsanov transformation, we arrive at the Gisin-Percival state diffusion equation [N. Gisin and J. Percival, J. Phys. A 167, 315 (1992)]. This approach also yields an explicit solution of the Gisin-Percival equation, in terms of the Hudson-Parthasarathy unitary process and a randomized Weyl displacement process. Irreversible dynamics of system density operators described by the well-known Gorini-Kossakowski-Sudarshan-Lindblad master equation is unraveled by coarse-graining over the Gisin-Percival quantum state trajectories.

Recursion equations in predicting band width under gradient elution.

PubMed

Liang, Heng; Liu, Ying

2004-06-18

The evolution of solute zone under gradient elution is a typical problem of non-linear continuity equation since the local diffusion coefficient and local migration velocity of the mass cells of solute zones are the functions of position and time due to space- and time-variable mobile phase composition. In this paper, based on the mesoscopic approaches (Lagrangian description, the continuity theory and the local equilibrium assumption), the evolution of solute zones in space- and time-dependent fields is described by the iterative addition of local probability density of the mass cells of solute zones. Furthermore, on macroscopic levels, the recursion equations have been proposed to simulate zone migration and spreading in reversed-phase high-performance liquid chromatography (RP-HPLC) through directly relating local retention factor and local diffusion coefficient to local mobile phase concentration. This new approach differs entirely from the traditional theories on plate concept with Eulerian description, since band width recursion equation is actually the accumulation of local diffusion coefficients of solute zones to discrete-time slices. Recursion equations and literature equations were used in dealing with same experimental data in RP-HPLC, and the comparison results show that the recursion equations can accurately predict band width under gradient elution.

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Theory of diffusion of active particles that move at constant speed in two dimensions.

PubMed

Sevilla, Francisco J; Gómez Nava, Luis A

2014-08-01

Starting from a Langevin description of active particles that move with constant speed in infinite two-dimensional space and its corresponding Fokker-Planck equation, we develop a systematic method that allows us to obtain the coarse-grained probability density of finding a particle at a given location and at a given time in arbitrary short-time regimes. By going beyond the diffusive limit, we derive a generalization of the telegrapher equation. Such generalization preserves the hyperbolic structure of the equation and incorporates memory effects in the diffusive term. While no difference is observed for the mean-square displacement computed from the two-dimensional telegrapher equation and from our generalization, the kurtosis results in a sensible parameter that discriminates between both approximations. We carry out a comparative analysis in Fourier space that sheds light on why the standard telegrapher equation is not an appropriate model to describe the propagation of particles with constant speed in dispersive media.

On the Role of Built-in Electric Fields on the Ignition of Oxide Coated NanoAluminum: Ion Mobility versus Fickian Diffusion

DTIC Science & Technology

2010-01-01

on Al ion diffu- sion can be computed using the Nernst –Planck equation . The Nernst –Plank equation is given in Eq. 4,22 J = − D dC dx − zFDC RT d dx...The use of the bulk diffusion equation is reason- able since during the time scales considered the movement of only the atoms initially on the surface

A meshless method for solving two-dimensional variable-order time fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Tayebi, A.; Shekari, Y.; Heydari, M. H.

2017-07-01

Several physical phenomena such as transformation of pollutants, energy, particles and many others can be described by the well-known convection-diffusion equation which is a combination of the diffusion and advection equations. In this paper, this equation is generalized with the concept of variable-order fractional derivatives. The generalized equation is called variable-order time fractional advection-diffusion equation (V-OTFA-DE). An accurate and robust meshless method based on the moving least squares (MLS) approximation and the finite difference scheme is proposed for its numerical solution on two-dimensional (2-D) arbitrary domains. In the time domain, the finite difference technique with a θ-weighted scheme and in the space domain, the MLS approximation are employed to obtain appropriate semi-discrete solutions. Since the newly developed method is a meshless approach, it does not require any background mesh structure to obtain semi-discrete solutions of the problem under consideration, and the numerical solutions are constructed entirely based on a set of scattered nodes. The proposed method is validated in solving three different examples including two benchmark problems and an applied problem of pollutant distribution in the atmosphere. In all such cases, the obtained results show that the proposed method is very accurate and robust. Moreover, a remarkable property so-called positive scheme for the proposed method is observed in solving concentration transport phenomena.

Flow regimes for fluid injection into a confined porous medium

DOE PAGES

Zheng, Zhong; Guo, Bo; Christov, Ivan C.; ...

2015-02-24

We report theoretical and numerical studies of the flow behaviour when a fluid is injected into a confined porous medium saturated with another fluid of different density and viscosity. For a two-dimensional configuration with point source injection, a nonlinear convection–diffusion equation is derived to describe the time evolution of the fluid–fluid interface. In the early time period, the fluid motion is mainly driven by the buoyancy force and the governing equation is reduced to a nonlinear diffusion equation with a well-known self-similar solution. In the late time period, the fluid flow is mainly driven by the injection, and the governingmore » equation is approximated by a nonlinear hyperbolic equation that determines the global spreading rate; a shock solution is obtained when the injected fluid is more viscous than the displaced fluid, whereas a rarefaction wave solution is found when the injected fluid is less viscous. In the late time period, we also obtain analytical solutions including the diffusive term associated with the buoyancy effects (for an injected fluid with a viscosity higher than or equal to that of the displaced fluid), which provide the structure of the moving front. Numerical simulations of the convection–diffusion equation are performed; the various analytical solutions are verified as appropriate asymptotic limits, and the transition processes between the individual limits are demonstrated.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions.

PubMed

Péraud, Jean-Philippe; Nonaka, Andrew J; Bell, John B; Donev, Aleksandar; Garcia, Alejandro L

2017-10-10

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson-Nernst-Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation-anion diffusion coefficient. Specifically, we predict a nonzero cation-anion Maxwell-Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye-Huckel-Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced "giant" velocity fluctuations and reduced fluctuations of salt concentration.

Fluctuation-enhanced electric conductivity in electrolyte solutions

PubMed Central

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; Donev, Aleksandar; Garcia, Alejandro L.

2017-01-01

We analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell–Stefan coefficient proportional to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Finally, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration. PMID:28973890

Edge-based nonlinear diffusion for finite element approximations of convection-diffusion equations and its relation to algebraic flux-correction schemes.

PubMed

Barrenechea, Gabriel R; Burman, Erik; Karakatsani, Fotini

2017-01-01

For the case of approximation of convection-diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The diffusion operator is shown to be Lipschitz continuous and linearity preserving. Using these properties we provide a full stability and error analysis, which, in the diffusion dominated regime, shows existence, uniqueness and optimal convergence. Then the algebraic flux correction method is recalled and we show that the present method can be interpreted as an algebraic flux correction method for a particular definition of the flux limiters. The performance of the method is illustrated on some numerical test cases in two space dimensions.

Fractal Model of Fission Product Release in Nuclear Fuel

NASA Astrophysics Data System (ADS)

Stankunas, Gediminas

2012-09-01

A model of fission gas migration in nuclear fuel pellet is proposed. Diffusion process of fission gas in granular structure of nuclear fuel with presence of inter-granular bubbles in the fuel matrix is simulated by fractional diffusion model. The Grunwald-Letnikov derivative parameter characterizes the influence of porous fuel matrix on the diffusion process of fission gas. A finite-difference method for solving fractional diffusion equations is considered. Numerical solution of diffusion equation shows correlation of fission gas release and Grunwald-Letnikov derivative parameter. Calculated profile of fission gas concentration distribution is similar to that obtained in the experimental studies. Diffusion of fission gas is modeled for real RBMK-1500 fuel operation conditions. A functional dependence of Grunwald-Letnikov derivative parameter with fuel burn-up is established.

Thermodynamics of viscoelastic rate-type fluids with stress diffusion

NASA Astrophysics Data System (ADS)

Málek, Josef; Průša, Vít; Skřivan, Tomáš; Süli, Endre

2018-02-01

We propose thermodynamically consistent models for viscoelastic fluids with a stress diffusion term. In particular, we derive variants of compressible/incompressible Maxwell/Oldroyd-B models with a stress diffusion term in the evolution equation for the extra stress tensor. It is shown that the stress diffusion term can be interpreted either as a consequence of a nonlocal energy storage mechanism or as a consequence of a nonlocal entropy production mechanism, while different interpretations of the stress diffusion mechanism lead to different evolution equations for the temperature. The benefits of the knowledge of the thermodynamical background of the derived models are documented in the study of nonlinear stability of equilibrium rest states. The derived models open up the possibility to study fully coupled thermomechanical problems involving viscoelastic rate-type fluids with stress diffusion.

Dusty Pair Plasma—Wave Propagation and Diffusive Transition of Oscillations

NASA Astrophysics Data System (ADS)

Atamaniuk, Barbara; Turski, Andrzej J.

2011-11-01

The crucial point of the paper is the relation between equilibrium distributions of plasma species and the type of propagation or diffusive transition of plasma response to a disturbance. The paper contains a unified treatment of disturbance propagation (transport) in the linearized Vlasov electron-positron and fullerene pair plasmas containing charged dust impurities, based on the space-time convolution integral equations. Electron-positron-dust/ion (e-p-d/i) plasmas are rather widespread in nature. Space-time responses of multi-component linearized Vlasov plasmas on the basis of multiple integral equations are invoked. An initial-value problem for Vlasov-Poisson/Ampère equations is reduced to the one multiple integral equation and the solution is expressed in terms of forcing function and its space-time convolution with the resolvent kernel. The forcing function is responsible for the initial disturbance and the resolvent is responsible for the equilibrium velocity distributions of plasma species. By use of resolvent equations, time-reversibility, space-reflexivity and the other symmetries are revealed. The symmetries carry on physical properties of Vlasov pair plasmas, e.g., conservation laws. Properly choosing equilibrium distributions for dusty pair plasmas, we can reduce the resolvent equation to: (i) the undamped dispersive wave equations, (ii) and diffusive transport equations of oscillations.

A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION. (R825689C072)

EPA Science Inventory

Abstract

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed a...

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.

2018-03-01

In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.

Liquefaction of Saturated Soil and the Diffusion Equation

NASA Astrophysics Data System (ADS)

Sawicki, Andrzej; Sławińska, Justyna

2015-06-01

The paper deals with the diffusion equation for pore water pressures with the source term, which is widely promoted in the marine engineering literature. It is shown that such an equation cannot be derived in a consistent way from the mass balance and the Darcy law. The shortcomings of the artificial source term are pointed out, including inconsistencies with experimental data. It is concluded that liquefaction and the preceding process of pore pressure generation and the weakening of the soil skeleton should be described by constitutive equations within the well-known framework of applied mechanics. Relevant references are provided

Transport mechanisms of contaminants released from fine sediment in rivers

NASA Astrophysics Data System (ADS)

Cheng, Pengda; Zhu, Hongwei; Zhong, Baochang; Wang, Daozeng

2015-12-01

Contaminants released from sediment into rivers are one of the main problems to study in environmental hydrodynamics. For contaminants released into the overlying water under different hydrodynamic conditions, the mechanical mechanisms involved can be roughly divided into convective diffusion, molecular diffusion, and adsorption/desorption. Because of the obvious environmental influence of fine sediment (D_{90}= 0.06 mm), non-cohesive fine sediment, and cohesive fine sediment are researched in this paper, and phosphorus is chosen for a typical adsorption of a contaminant. Through theoretical analysis of the contaminant release process, according to different hydraulic conditions, the contaminant release coupling mathematical model can be established by the N-S equation, the Darcy equation, the solute transport equation, and the adsorption/desorption equation. Then, the experiments are completed in an open water flume. The simulation results and experimental results show that convective diffusion dominates the contaminant release both in non-cohesive and cohesive fine sediment after their suspension, and that they contribute more than 90 % of the total release. Molecular diffusion and desorption have more of a contribution for contaminant release from unsuspended sediment. In unsuspension sediment, convective diffusion is about 10-50 times larger than molecular diffusion during the initial stages under high velocity; it is close to molecular diffusion in the later stages. Convective diffusion is about 6 times larger than molecular diffusion during the initial stages under low velocity, it is about a quarter of molecular diffusion in later stages, and has a similar level with desorption/adsorption. In unsuspended sediment, a seepage boundary layer exists below the water-sediment interface, and various release mechanisms in that layer mostly dominate the contaminant release process. In non-cohesive fine sediment, the depth of that layer increases linearly with shear stress. In cohesive fine sediment, the range seepage boundary is different from that in non-cohesive sediment, and that phenomenon is more obvious under a lower shear stress.

Linear response theory and transient fluctuation relations for diffusion processes: a backward point of view

NASA Astrophysics Data System (ADS)

Liu, Fei; Tong, Huan; Ma, Rui; Ou-Yang, Zhong-can

2010-12-01

A formal apparatus is developed to unify derivations of the linear response theory and a variety of transient fluctuation relations for continuous diffusion processes from a backward point of view. The basis is a perturbed Kolmogorov backward equation and the path integral representation of its solution. We find that these exact transient relations could be interpreted as a consequence of a generalized Chapman-Kolmogorov equation, which intrinsically arises from the Markovian characteristic of diffusion processes.

New explicit equations for the accurate calculation of the growth and evaporation of hydrometeors by the diffusion of water vapor

NASA Technical Reports Server (NTRS)

Srivastava, R. C.; Coen, J. L.

1992-01-01

The traditional explicit growth equation has been widely used to calculate the growth and evaporation of hydrometeors by the diffusion of water vapor. This paper reexamines the assumptions underlying the traditional equation and shows that large errors (10-30 percent in some cases) result if it is used carelessly. More accurate explicit equations are derived by approximating the saturation vapor-density difference as a quadratic rather than a linear function of the temperature difference between the particle and ambient air. These new equations, which reduce the error to less than a few percent, merit inclusion in a broad range of atmospheric models.

A Simple Mathematical Model Inspired by the Purkinje Cells: From Delayed Travelling Waves to Fractional Diffusion.

PubMed

Dipierro, Serena; Valdinoci, Enrico

2018-07-01

Recently, several experiments have demonstrated the existence of fractional diffusion in the neuronal transmission occurring in the Purkinje cells, whose malfunctioning is known to be related to the lack of voluntary coordination and the appearance of tremors. Also, a classical mathematical feature is that (fractional) parabolic equations possess smoothing effects, in contrast with the case of hyperbolic equations, which typically exhibit shocks and discontinuities. In this paper, we show how a simple toy-model of a highly ramified structure, somehow inspired by that of the Purkinje cells, may produce a fractional diffusion via the superposition of travelling waves that solve a hyperbolic equation. This could suggest that the high ramification of the Purkinje cells might have provided an evolutionary advantage of "smoothing" the transmission of signals and avoiding shock propagations (at the price of slowing a bit such transmission). Although an experimental confirmation of the possibility of such evolutionary advantage goes well beyond the goals of this paper, we think that it is intriguing, as a mathematical counterpart, to consider the time fractional diffusion as arising from the superposition of delayed travelling waves in highly ramified transmission media. The case of a travelling concave parabola with sufficiently small curvature is explicitly computed. The new link that we propose between time fractional diffusion and hyperbolic equation also provides a novelty with respect to the usual paradigm relating time fractional diffusion with parabolic equations in the limit. This paper is written in such a way as to be of interest to both biologists and mathematician alike. In order to accomplish this aim, both complete explanations of the objects considered and detailed lists of references are provided.

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Angstmann, C.N.; Donnelly, I.C.; Henry, B.I., E-mail: B.Henry@unsw.edu.au

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also showmore » that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.« less

Birth-jump processes and application to forest fire spotting.

PubMed

Hillen, T; Greese, B; Martin, J; de Vries, G

2015-01-01

Birth-jump models are designed to describe population models for which growth and spatial spread cannot be decoupled. A birth-jump model is a nonlinear integro-differential equation. We present two different derivations of this equation, one based on a random walk approach and the other based on a two-compartmental reaction-diffusion model. In the case that the redistribution kernels are highly concentrated, we show that the integro-differential equation can be approximated by a reaction-diffusion equation, in which the proliferation rate contributes to both the diffusion term and the reaction term. We completely solve the corresponding critical domain size problem and the minimal wave speed problem. Birth-jump models can be applied in many areas in mathematical biology. We highlight an application of our results in the context of forest fire spread through spotting. We show that spotting increases the invasion speed of a forest fire front.

Reexamination of relaxation of spins due to a magnetic field gradient: Identity of the Redfield and Torrey theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, R.; Rohm, Ryan M.; Swank, C. M.

2011-02-15

There is an extensive literature on magnetic-gradient-induced spin relaxation. Cates, Schaefer, and Happer, in a seminal publication, have solved the problem in the regime where diffusion theory (the Torrey equation) is applicable using an expansion of the density matrix in diffusion equation eigenfunctions and angular momentum tensors. McGregor has solved the problem in the same regime using a slightly more general formulation using the Redfield theory formulated in terms of the autocorrelation function of the fluctuating field seen by the spins and calculating the correlation functions using the diffusion-theory Green's function. The results of both calculations were shown to agreemore » for a special case. In the present work, we show that the eigenfunction expansion of the Torrey equation yields the expansion of the Green's function for the diffusion equation, thus showing the identity of this approach with that of the Redfield theory. The general solution can also be obtained directly from the Torrey equation for the density matrix. Thus, the physical content of the Redfield and Torrey approaches are identical. We then introduce a more general expression for the position autocorrelation function of particles moving in a closed cell, extending the range of applicability of the theory.« less

Inhibitory effect on the uptake and diffusion of Cd(2+) onto soybean hull sorbent in Cd-Pb binary sorption systems.

PubMed

Módenes, Aparecido N; Espinoza-Quiñones, Fernando R; Colombo, Andréia; Geraldi, Claudinéia L; Trigueros, Daniela E G

2015-05-01

The uptake of Cd(2+) and Pb(2+) ions by a soybean hull (SH) biosorbent in single and binary systems has been investigated. Sorption tests regarding SH in natura and chemically treated were carried out testing a suitable value range of solution pH, sorption temperature and shaking velocity. Sorption capacity is improved at pH 4, 30 °C temperature and 100 rpm. When a strong base is applied, a related-to-untreated SH increasing of 20% in the sorption capacity of Pb(2+) ions was observed, but with poor results for Cd(2+) uptake. Additionally, a relatively strong decreasing in both sorption capacities of Pb(2+) and Cd(2+) ions was evidenced for all acidic treatments. Regarding untreated SH, kinetic sorption data of both metals were well-interpreted by a pseudo second-order model and a rate-limiting step on the basis of an intra-particle diffusion model was suggested to occur. An inhibitory effect of Pb(2+) diffusion over Cd(2+) one was observed, limiting to reach the obtained maximum sorption capacity in single system. Maximum adsorption capacities of 0.49 and 0.67mequivg(-1) for Cd(2+) and Pb(2+), respectively, were predicted by the Langmuir isotherm model that reproduced well the equilibrium sorption data for single systems. The inhibitory effect of one metal over the other one was verified in equilibrium sorption data for binary systems interpreted on the basis of a modified extended Langmuir isotherm model, predicting changes in metal affinity onto the SH surface. Finally, SH is an alternative biosorbent with a great potential for the wastewater treatment containing cadmium and lead ions. Copyright © 2015 Elsevier Ltd. All rights reserved.

Transport and concentration controls for chloride, strontium, potassium and lead in Uvas Creek, a small cobble-bed stream in Santa Clara County, California, U.S.A. 2. Mathematical modeling

USGS Publications Warehouse

Jackman, A.P.; Walters, R.A.; Kennedy, V.C.

1984-01-01

Three models describing solute transport of conservative ion species and another describing transport of species which adsorb linearly and reversibly on bed sediments are developed and tested. The conservative models are based on three different conceptual models of the transient storage of solute in the bed. One model assumes the bed to be a well-mixed zone with flux of solute into the bed proportional to the difference between stream concentration and bed concentration. The second model assumes solute in the bed is transported by a vertical diffusion process described by Fick's law. The third model assumes that convection occurs in a selected portion of the bed while the mechanism of the first model functions everywhere. The model for adsorbing species assumes that the bed consists of particles of uniform size with the rate of uptake controlled by an intraparticle diffusion process. All models are tested using data collected before, during and after a 24-hr. pulse injection of chloride, strontium, potassium and lead ions into Uvas Creek near Morgan Hill, California, U.S.A. All three conservative models accurately predict chloride ion concentrations in the stream. The model employing the diffusion mechanism for bed transport predicts better than the others. The adsorption model predicts both strontium and potassium ion concentrations well during the injection of the pulse but somewhat overestimates the observed concentrations after the injection ceases. The overestimation may be due to the convection of solute deep into the bed where it is retained longer than the 3-week post-injection observation period. The model, when calibrated for strontium, predicts potassium equally well when the adsorption equilibrium constant for strontium is replaced by that for potassium. ?? 1984.

Characterization of large-pore polymeric supports for use in perfusion biochromatography.

PubMed

Whitney, D; McCoy, M; Gordon, N; Afeyan, N

1998-05-22

Perfusion chromatography is uniquely characterized by the flow of a portion of the column eluent directly through the resin in the packed bed. The benefits of this phenomenon and some of the properties of perfusive resins have been described before, and can be summarized as enhanced mass transport to interior binding sites. Here we extend the understanding of this phenomenon by comparing resins with different pore size distributions. Resins are chosen to give approximately the same specific pore volumes (as shown in the characterization section) but the varying contribution of large pores is used to control the amount of liquid flowing through the beads. POROS R1 has the largest contribution of throughpores, and therefore the greatest intraparticle flow. POROS R2 has a lower contribution of throughpores, and a higher surface area coming from a greater population of diffusive pores, but still shows significant mass transport enhancements relative to a purely diffusive control. Oligo R3 is dominated by a high population of diffusive pores, and is used comparatively as a non-perfusive resin. Although the pore size distribution can be engineered to control mass transport rates, the resulting surface area is not the only means by which binding capacity can be controlled. Surface coatings are employed to increase binding capacity without fundamentally altering the mass transport properties. Models are used to describe the amount of flow transecting the beads, and comparisons of coated resins to uncoated (polystyrene) resins leads to the conclusion that these coatings do not obstruct the throughpore structures. This is an important conclusion since the binding capacity of the coated product, in some cases, is shown to be over 10-fold higher than the precursor polystyrene scaffold (i.e., POROS R1 or POROS R2).

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

NASA Astrophysics Data System (ADS)

Gyrya, V.; Lipnikov, K.

2017-11-01

We present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE PAGES

Gyrya, V.; Lipnikov, K.

2017-07-18

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

The arbitrary order mimetic finite difference method for a diffusion equation with a non-symmetric diffusion tensor

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gyrya, V.; Lipnikov, K.

Here, we present the arbitrary order mimetic finite difference (MFD) discretization for the diffusion equation with non-symmetric tensorial diffusion coefficient in a mixed formulation on general polygonal meshes. The diffusion tensor is assumed to be positive definite. The asymmetry of the diffusion tensor requires changes to the standard MFD construction. We also present new approach for the construction that guarantees positive definiteness of the non-symmetric mass matrix in the space of discrete velocities. The numerically observed convergence rate for the scalar quantity matches the predicted one in the case of the lowest order mimetic scheme. For higher orders schemes, wemore » observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor. The new scheme was also tested on a time-dependent problem modeling the Hall effect in the resistive magnetohydrodynamics.« less

Maximum Path Information and Fokker Planck Equation

NASA Astrophysics Data System (ADS)

Li, Wei; Wang A., Q.; LeMehaute, A.

2008-04-01

We present a rigorous method to derive the nonlinear Fokker-Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang [Chaos, Solitons & Fractals 23 (2005) 1253] for smooth or quasi-smooth irregular dynamics evolving in Markovian process. The FP equation obtained may take two different but equivalent forms. It was also found that the diffusion constant may depend on both q (the index of Tsallis entropy [J. Stat. Phys. 52 (1988) 479] and the time t.

Molecular dynamics on diffusive time scales from the phase-field-crystal equation.

PubMed

Chan, Pak Yuen; Goldenfeld, Nigel; Dantzig, Jon

2009-03-01

We extend the phase-field-crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of them. By solving the dynamical equation of the model, which is a partial differential equation, we are essentially performing molecular dynamics simulations on diffusive time scales. To illustrate this approach, we calculate the two-point correlation function of a fluid.

Non-Markovian Effects in Turbulent Diffusion in Magnetized Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zagorodny, Anatoly; Weiland, Jan

2009-10-08

The derivation of the kinetic equations for inhomogeneous plasma in an external magnetic field is presented. The Fokker-Planck-type equations with the non-Markovian kinetic coefficients are proposed. In the time-local limit (small correlation times with respect to the distribution function relaxation time) the relations obtained recover the results known from the appropriate quasilinear theory and the Dupree-Weinstock theory of plasma turbulence. The equations proposed are used to describe zonal flow generation and to estimate the diffusion coefficient for saturated turbulence.

Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations.

PubMed

Asinari, Pietro

2009-11-01

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

A cross-diffusion system derived from a Fokker-Planck equation with partial averaging

NASA Astrophysics Data System (ADS)

Jüngel, Ansgar; Zamponi, Nicola

2017-02-01

A cross-diffusion system for two components with a Laplacian structure is analyzed on the multi-dimensional torus. This system, which was recently suggested by P.-L. Lions, is formally derived from a Fokker-Planck equation for the probability density associated with a multi-dimensional Itō process, assuming that the diffusion coefficients depend on partial averages of the probability density with exponential weights. A main feature is that the diffusion matrix of the limiting cross-diffusion system is generally neither symmetric nor positive definite, but its structure allows for the use of entropy methods. The global-in-time existence of positive weak solutions is proved and, under a simplifying assumption, the large-time asymptotics is investigated.

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

NASA Astrophysics Data System (ADS)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

Do the Particles of an Ideal Gas Collide?

ERIC Educational Resources Information Center

Lesk, Arthur M.

1974-01-01

Describes the collisional properties as a logically essential component of the ideal gas model since an actual intraparticle process cannot support observable anisotropic velocity distributions without collisions taken into account. (CC)

Functionalized granular activated carbon and surface complexation with chromates and bi-chromates in wastewater.

PubMed

Singha, Somdutta; Sarkar, Ujjaini; Luharuka, Pallavi

2013-03-01

Cr(VI) is present in the aqueous medium as chromate (CrO4(2-)) and bi-chromate (HCrO4(-)). Functionalized granular activated carbons (FACs) are used as adsorbents in the treatment of wastewaters containing hexavalent chromium. The FACs are prepared by chemical modifications of granular activated carbons (GACs) using functionalizing agents like HNO3, HCl and HF. The Brunauer, Emmett and Teller surface areas of FAC-HCl (693.5m(2)/g), FAC-HNO3 (648.8m(2)/g) and FAC-HF (726.2m(2)/g) are comparable to the GAC (777.7m(2)/g). But, the adsorption capacity of each of the FAC-HNO3, FAC-HCl and FAC-HF is found to be higher than the GAC. The functional groups play an important role in the adsorption process and pH has practically no role in this specific case. The FACs have hydrophilic protonated external surfaces in particular, along with the functional surface sites capable to make complexes with the CrO4(2-) and HCrO4(-) present. Surface complex formation is maximized in the order FAC-HNO3>FAC-HF>FAC-HCl, in proportion to the total surface acidity. This is also confirmed by the well-known pseudo second-order kinetic model. Physi-sorption equilibrium isotherms are parameterized by using standard Freundlich and Langmuir models. Langmuir fits better. The formation of surface complexes with the functional groups and hexavalent chromium is also revealed in the images of field emission scanning electron micrograph; energy dispersive X-ray spectroscopy and Fourier transform infrared spectroscopy analysis after adsorption. The intra-particle diffusion is not the only rate-controlling factor. The Boyd's film diffusion model fits very well with R(2) as high as 98.1% for FAC-HNO3. This result demonstrates that the functionalization of the GAC by acid treatments would increase the diffusion rate, predominantly with a boundary layer diffusion effect. Copyright © 2013 Elsevier B.V. All rights reserved.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brantley, P S

2006-09-27

We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinarymore » differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.« less

Interface- and discontinuity-aware numerical schemes for plasma 3-T radiation diffusion in two and three dimensions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dai, William W., E-mail: dai@lanl.gov; Scannapieco, Anthony J.

2015-11-01

A set of numerical schemes is developed for two- and three-dimensional time-dependent 3-T radiation diffusion equations in systems involving multi-materials. To resolve sub-cell structure, interface reconstruction is implemented within any cell that has more than one material. Therefore, the system of 3-T radiation diffusion equations is solved on two- and three-dimensional polyhedral meshes. The focus of the development is on the fully coupling between radiation and material, the treatment of nonlinearity in the equations, i.e., in the diffusion terms and source terms, treatment of the discontinuity across cell interfaces in material properties, the formulations for both transient and steady states,more » the property for large time steps, and second order accuracy in both space and time. The discontinuity of material properties between different materials is correctly treated based on the governing physics principle for general polyhedral meshes and full nonlinearity. The treatment is exact for arbitrarily strong discontinuity. The scheme is fully nonlinear for the full nonlinearity in the 3-T diffusion equations. Three temperatures are fully coupled and are updated simultaneously. The scheme is general in two and three dimensions on general polyhedral meshes. The features of the scheme are demonstrated through numerical examples for transient problems and steady states. The effects of some simplifications of numerical schemes are also shown through numerical examples, such as linearization, simple average of diffusion coefficient, and approximate treatment for the coupling between radiation and material.« less

A numerical solution for the diffusion equation in hydrogeologic systems

USGS Publications Warehouse

Ishii, A.L.; Healy, R.W.; Striegl, Robert G.

1989-01-01

The documentation of a computer code for the numerical solution of the linear diffusion equation in one or two dimensions in Cartesian or cylindrical coordinates is presented. Applications of the program include molecular diffusion, heat conduction, and fluid flow in confined systems. The flow media may be anisotropic and heterogeneous. The model is formulated by replacing the continuous linear diffusion equation by discrete finite-difference approximations at each node in a block-centered grid. The resulting matrix equation is solved by the method of preconditioned conjugate gradients. The conjugate gradient method does not require the estimation of iteration parameters and is guaranteed convergent in the absence of rounding error. The matrixes are preconditioned to decrease the steps to convergence. The model allows the specification of any number of boundary conditions for any number of stress periods, and the output of a summary table for selected nodes showing flux and the concentration of the flux quantity for each time step. The model is written in a modular format for ease of modification. The model was verified by comparison of numerical and analytical solutions for cases of molecular diffusion, two-dimensional heat transfer, and axisymmetric radial saturated fluid flow. Application of the model to a hypothetical two-dimensional field situation of gas diffusion in the unsaturated zone is demonstrated. The input and output files are included as a check on program installation. The definition of variables, input requirements, flow chart, and program listing are included in the attachments. (USGS)

Development of a Rational Modeling Approach for the Design, and Optimization of the Multifiltration Unit. Volume 1

NASA Technical Reports Server (NTRS)

Hand, David W.; Crittenden, John C.; Ali, Anisa N.; Bulloch, John L.; Hokanson, David R.; Parrem, David L.

1996-01-01

This thesis includes the development and verification of an adsorption model for analysis and optimization of the adsorption processes within the International Space Station multifiltration beds. The fixed bed adsorption model includes multicomponent equilibrium and both external and intraparticle mass transfer resistances. Single solute isotherm parameters were used in the multicomponent equilibrium description to predict the competitive adsorption interactions occurring during the adsorption process. The multicomponent equilibrium description used the Fictive Component Analysis to describe adsorption in unknown background matrices. Multicomponent isotherms were used to validate the multicomponent equilibrium description. Column studies were used to develop and validate external and intraparticle mass transfer parameter correlations for compounds of interest. The fixed bed model was verified using a shower and handwash ersatz water which served as a surrogate to the actual shower and handwash wastewater.

On the Maxwell-Stefan approach to diffusion: a general resolution in the transient regime for one-dimensional systems.

PubMed

Leonardi, Erminia; Angeli, Celestino

2010-01-14

The diffusion process in a multicomponent system can be formulated in a general form by the generalized Maxwell-Stefan equations. This formulation is able to describe the diffusion process in different systems, such as, for instance, bulk diffusion (in the gas, liquid, and solid phase) and diffusion in microporous materials (membranes, zeolites, nanotubes, etc.). The Maxwell-Stefan equations can be solved analytically (only in special cases) or by numerical approaches. Different numerical strategies have been previously presented, but the number of diffusing species is normally restricted, with only few exceptions, to three in bulk diffusion and to two in microporous systems, unless simplifications of the Maxwell-Stefan equations are considered. In the literature, a large effort has been devoted to the derivation of the analytic expression of the elements of the Fick-like diffusion matrix and therefore to the symbolic inversion of a square matrix with dimensions n x n (n being the number of independent components). This step, which can be easily performed for n = 2 and remains reasonable for n = 3, becomes rapidly very complex in problems with a large number of components. This paper addresses the problem of the numerical resolution of the Maxwell-Stefan equations in the transient regime for a one-dimensional system with a generic number of components, avoiding the definition of the analytic expression of the elements of the Fick-like diffusion matrix. To this aim, two approaches have been implemented in a computational code; the first is the simple finite difference second-order accurate in time Crank-Nicolson scheme for which the full mathematical derivation and the relevant final equations are reported. The second is based on the more accurate backward differentiation formulas, BDF, or Gear's method (Shampine, L. F. ; Gear, C. W. SIAM Rev. 1979, 21, 1.), as implemented in the Livermore solver for ordinary differential equations, LSODE (Hindmarsh, A. C. Serial Fortran Solvers for ODE Initial Value Problems, Technical Report; https://computation.llnl.gov/casc/odepack/odepack_ home.html (2006).). Both methods have been applied to a series of specific problems, such as bulk diffusion of acetone and methanol through stagnant air, uptake of two components on a microporous material in a model system, and permeation across a microporous membrane in model systems, both with the aim to validate the method and to add new information to the comprehension of the peculiar behavior of these systems. The approach is validated by comparison with different published results and with analytic expressions for the steady-state concentration profiles or fluxes in particular systems. The possibility to treat a generic number of components (the limitation being essentially the computational power) is also tested, and results are reported on the permeation of a five component mixture through a membrane in a model system. It is worth noticing that the algorithm here reported can be applied also to the Fick formulation of the diffusion problem with concentration-dependent diffusion coefficients.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

DOE PAGES

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen; ...

2017-05-15

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Predicting Ga and Cu Profiles in Co-Evaporated Cu(In,Ga)Se 2 Using Modified Diffusion Equations and a Spreadsheet

DOE Office of Scientific and Technical Information (OSTI.GOV)

Repins, Ingrid L.; Harvey, Steve; Bowers, Karen

Cu(In,Ga)Se 2(CIGS) photovoltaic absorbers frequently develop Ga gradients during growth. These gradients vary as a function of growth recipe, and are important to device performance. Prediction of Ga profiles using classic diffusion equations is not possible because In and Ga atoms occupy the same lattice sites and thus diffuse interdependently, and there is not yet a detailed experimental knowledge of the chemical potential as a function of composition that describes this interaction. Here, we show how diffusion equations can be modified to account for site sharing between In and Ga atoms. The analysis has been implemented in an Excel spreadsheet,more » and outputs predicted Cu, In, and Ga profiles for entered deposition recipes. A single set of diffusion coefficients and activation energies are chosen, such that simulated elemental profiles track with published data and those from this study. Extent and limits of agreement between elemental profiles predicted from the growth recipes and the spreadsheet tool are demonstrated.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE PAGES

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.; ...

2017-09-26

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Fluctuation-enhanced electric conductivity in electrolyte solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Péraud, Jean-Philippe; Nonaka, Andrew J.; Bell, John B.

In this work, we analyze the effects of an externally applied electric field on thermal fluctuations for a binary electrolyte fluid. We show that the fluctuating Poisson–Nernst–Planck (PNP) equations for charged multispecies diffusion coupled with the fluctuating fluid momentum equation result in enhanced charge transport via a mechanism distinct from the well-known enhancement of mass transport that accompanies giant fluctuations. Although the mass and charge transport occurs by advection by thermal velocity fluctuations, it can macroscopically be represented as electrodiffusion with renormalized electric conductivity and a nonzero cation–anion diffusion coefficient. Specifically, we predict a nonzero cation–anion Maxwell– Stefan coefficient proportionalmore » to the square root of the salt concentration, a prediction that agrees quantitatively with experimental measurements. The renormalized or effective macroscopic equations are different from the starting PNP equations, which contain no cross-diffusion terms, even for rather dilute binary electrolytes. At the same time, for infinitely dilute solutions the renormalized electric conductivity and renormalized diffusion coefficients are consistent and the classical PNP equations with renormalized coefficients are recovered, demonstrating the self-consistency of the fluctuating hydrodynamics equations. Our calculations show that the fluctuating hydrodynamics approach recovers the electrophoretic and relaxation corrections obtained by Debye–Huckel–Onsager theory, while elucidating the physical origins of these corrections and generalizing straightforwardly to more complex multispecies electrolytes. Lastly, we show that strong applied electric fields result in anisotropically enhanced “giant” velocity fluctuations and reduced fluctuations of salt concentration.« less

Viscosity and diffusivity in melts: from unary to multicomponent systems

NASA Astrophysics Data System (ADS)

Chen, Weimin; Zhang, Lijun; Du, Yong; Huang, Baiyun

2014-05-01

Viscosity and diffusivity, two important transport coefficients, are systematically investigated from unary melt to binary to multicomponent melts in the present work. By coupling with Kaptay's viscosity equation of pure liquid metals and effective radii of diffusion species, the Sutherland equation is modified by taking the size effect into account, and further derived into an Arrhenius formula for the convenient usage. Its reliability for predicting self-diffusivity and impurity diffusivity in unary liquids is then validated by comparing the calculated self-diffusivities and impurity diffusivities in liquid Al- and Fe-based alloys with the experimental and the assessed data. Moreover, the Kozlov model was chosen among various viscosity models as the most reliable one to reproduce the experimental viscosities in binary and multicomponent melts. Based on the reliable viscosities calculated from the Kozlov model, the modified Sutherland equation is utilized to predict the tracer diffusivities in binary and multicomponent melts, and validated in Al-Cu, Al-Ni and Al-Ce-Ni melts. Comprehensive comparisons between the calculated results and the literature data indicate that the experimental tracer diffusivities and the theoretical ones can be well reproduced by the present calculations. In addition, the vacancy-wind factor in binary liquid Al-Ni alloys with the increasing temperature is also discussed. What's more, the calculated inter-diffusivities in liquid Al-Cu, Al-Ni and Al-Ag-Cu alloys are also in excellent agreement with the measured and theoretical data. Comparisons between the simulated concentration profiles and the measured ones in Al-Cu, Al-Ce-Ni and Al-Ag-Cu melts are further used to validate the present calculation method.

Analytical study of fractional equations describing anomalous diffusion of energetic particles

NASA Astrophysics Data System (ADS)

Tawfik, A. M.; Fichtner, H.; Schlickeiser, R.; Elhanbaly, A.

2017-06-01

To present the main influence of anomalous diffusion on the energetic particle propagation, the fractional derivative model of transport is developed by deriving the fractional modified Telegraph and Rayleigh equations. Analytical solutions of the fractional modified Telegraph and the fractional Rayleigh equations, which are defined in terms of Caputo fractional derivatives, are obtained by using the Laplace transform and the Mittag-Leffler function method. The solutions of these fractional equations are given in terms of special functions like Fox’s H, Mittag-Leffler, Hermite and Hyper-geometric functions. The predicted travelling pulse solutions are discussed in each case for different values of fractional order.

An insight into the adsorption of diclofenac on different biochars: Mechanisms, surface chemistry, and thermodynamics.

PubMed

Lonappan, Linson; Rouissi, Tarek; Kaur Brar, Satinder; Verma, Mausam; Surampalli, Rao Y

2018-02-01

Biochars were prepared from feedstocks pinewood and pig manure. Biochar microparticles obtained through grinding were evaluated for the removal of emerging contaminant diclofenac (DCF) and the underlying mechanism were thoroughly studied. Characterization of biochar was carried out using particle size analyzer, SEM, BET, FT-IR, XRD, XPS and zeta potential instrument. Pig manure biochar (BC-PM) exhibited excellent removal efficiency (99.6%) over pine wood biochar (BC-PW) at 500 µg L -1 of DCF (environmentally significant concentration). Intraparticle diffusion was found to be the major process facilitated the adsorption. BC-PW followed pseudo first-order kinetics whereas BC-PM followed pseudo second-order kinetics. Pine wood biochar was largely affected by pH variations whereas for pig manure biochar, pH effects were minimal owing to its surface functional groups and DCF hydrophobicity. Thermodynamics, presence of co-existing ions, initial adsorbate concentration and particles size played substantial role in adsorption. Various isotherms models were also studied and results are presented. Copyright © 2017 Elsevier Ltd. All rights reserved.

Removal of fluoride from drinking water using aluminum hydroxide coated activated carbon prepared from bark of Morinda tinctoria

NASA Astrophysics Data System (ADS)

Amalraj, Augustine; Pius, Anitha

2017-10-01

The aim of this study is to design and develop a novel cost effective method for fluoride removal, applicable to rural areas of developing countries. Adsorption is widely considered as one of the appropriate technologies for water defluoridation. This study investigates the feasibility of using low-cost biomass based activated carbon from the bark of Morinda tinctoria coated with aluminum hydroxide (AHAC) for water defluoridation, at neutral pH range. Characterization of AHAC was done through IR, SEM with EDAX studies before and after fluoride treatment. The fluoride adsorption capacity of AHAC as a function of contact time, pH and initial fluoride concentration was investigated. The role of co-existing interfering ions also was studied. The isotherm and kinetic models were used to understand the nature of the fluoride adsorption onto AHAC. Freundlich isotherm and intra-particle diffusion were the best-fitting models for the adsorption of fluoride on AHAC. Fluoride adsorption kinetics well fitted with pseudo-second order model. The results showed excellent fluoride adsorption capacity was found to be 26.03 mg g-1 at neutral pH.

Adsorption of quinolone, tetracycline, and penicillin antibiotics from aqueous solution using activated carbons: Review.

PubMed

Ahmed, Muthanna J

2017-03-01

Antibiotics, an important type of pharmaceutical pollutant, have attracted many researchers to the study of their removal from aqueous solutions. Activated carbon (AC) has been widely used as highly effective adsorbent for antibiotics because of its large specific surface area, high porosity, and favorable pore size distribution. In this article, the adsorption performance of AC towards three major types of antibiotics such as tetracyclines, quinolones, and penicillins were reviewed. According to collected data, maximum adsorption capacities of 1340.8, 638.6, and 570.4mg/g were reported for tetracyclines, quinolones, and penicillins, respectively. The values of 1/n for Freundlich isotherm were less than unity, suggesting that the adsorption was nonlinear and favorable. Adsorption kinetics followed closely the pseudo-second-order model and analysis using the Weber-Morris model revealed that the intra-particle diffusion was not the only rate controlling step. AC adsorption demonstrated superior performance for all selected drugs, thus being efficient technology for treatment of these pollutants. Copyright © 2017 Elsevier B.V. All rights reserved.

Aluminum drinking water treatment residuals (Al-WTRs) as sorbent for mercury: Implications for soil remediation.

PubMed

Hovsepyan, Anna; Bonzongo, Jean-Claude J

2009-05-15

The potential of readily available and non-hazardous waste material, aluminum drinking water treatment residuals (Al-WTRs), to efficiently sorb and immobilize mercury (Hg) from aqueous solutions was evaluated. Al-WTR samples with average specific surface area of 48m(2)/g and internal micropore surface area of 120m(2)/g were used in a series of batch sorption experiments. Obtained sorption isotherms indicated a strong affinity of Hg for Al-WTRs. Using the Langmuir adsorption model, a relatively high maximum sorption capacity of 79mg Hg/g Al-WTRs was determined. Sorption kinetic data was best fit to a pseudo-first-order model, while the use of the Weber-Morris and Bangham models suggested that the intraparticle diffusion could be the rate-limiting step. Also, Al-WTRs effectively immoblized Hg in the pH range of 3-8. The results from these short-term experiments demonstrate that Al-WTRs can be effectively used to remove Hg from aqueous solutions. This ability points to the potential of Al-WTRs as a sorbent in soil remediation techniques based on Hg-immobilization.

Biosorption of Pb(II) from aqueous solution by Solanum melongena leaf powder as a low-cost biosorbent prepared from agricultural waste.

PubMed

Yuvaraja, Gutha; Krishnaiah, Nettem; Subbaiah, Munagapati Venkata; Krishnaiah, Abburi

2014-02-01

Solanum melongena leaves are relatively galore and used as inexpensive material. This paper presents the characterization and evaluation of potential of S. melongena leaf powder (SMLP) for removal of Pb(II) from aqueous solution as a function of pH, biomass dosage, initial metal ion concentration, contact time and temperature. Experimental data were analyzed in terms of three kinetic models such as the pseudo-first-order, pseudo-second-order and intraparticle diffusion models and the results showed that the biosorption processes of Pb(II) followed well pseudo-second-order kinetics. Langmuir and Freundlich isotherm models were applied to describe the biosorption process. Langmuir isotherm described the equilibrium data very well, with a maximum monolayer sorption capacity of 71.42 mg/g for Pb(II) ions at 323 K. The biosorption process was spontaneous and endothermic in nature with negative ΔG° (-8.746, -8.509 and -7.983 kJ/mol) and positive value for ΔH° (3.698 kJ/mol). Copyright © 2013 Elsevier B.V. All rights reserved.

Sorption of chlorophenols from aqueous solution by granular activated carbon, filter coal, pine and hardwood.

PubMed

Hossain, G S M; McLaughlan, R G

2012-09-01

Wood and coal, as low-cost sorbents, have been evaluated as an alternative to commercial granular activated carbon (GAC) for chlorophenol removal. Kinetic experiments indicated that filter coal had a significantly lower rate of uptake (approximately 10% of final uptake was achieved after three hours) than the other sorbents, owing to intra-particle diffusion limitations. The data fitted a pseudo-second-order model. Sorption capacity data showed that GAC had a high sorption capacity (294-467 mg g(-1)) compared with other sorbents (3.2-7.5 mg(g-1)). However, wood and coal had a greater sorption capacity per unit surface area than GAC. Sorption equilibrium data was best predicted using a Freundlich adsorption model. The sorption capacity for all sorbents was 2-chlorophenol < 4-chlorophenol < 2, 4-dichlorophenol, which correlates well with solute hydrophobicity, although the relative differences were much less for coal than the other sorbents. The results showed that pine, hardwood and filter coal can be used as sorbent materials for the removal of chlorophenol from water; however, kinetic considerations may limit the application of filter coal.

Nitrogen-functionalization biochars derived from wheat straws via molten salt synthesis: An efficient adsorbent for atrazine removal.

PubMed

Yang, Fan; Sun, Lili; Xie, Weiling; Jiang, Qun; Gao, Yan; Zhang, Wei; Zhang, Ying

2017-12-31

N-doped porous carbon sheets (NPCS) resulted from wheat straws are fabricated through using molten salts via the carbonization-functionalization progress, which show unique hierarchical structure, large pore volume and high surface area with affluent micropores. Results indicate that there exist many hierarchical pores consisting of the single carbon sheet with ultrathin nature, owing to the template role of molten salt mixtures at high temperature. Such superior structure can bring about desired performance of adsorption capacity of 82.8mg/g and quick adsorption rate of 1.43L/(gh) with an initial concentration of 35mg/L at 25°C. Langmuir and Freundlich models are adopted to interpret the adsorption behavior of atrazine and modified Freundlich and intraparticle diffusion (IPD) models are employed to characterize the dynamics of adsorption. Furthermore, nitrogen-functionalization biochars via molten salt synthesis should be further developed as a one-pot methodology to produce N-doped carbons, opening up a feasible approach for resource utilization of crop straws and other biomass wastes. Copyright © 2017 Elsevier B.V. All rights reserved.

Separative analyses of a chromatographic column packed with a core-shell adsorbent for lithium isotope separation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sugiyama, T.; Sugura, K.; Enokida, Y.

2015-03-15

Lithium-6 is used as a blanket material for sufficient tritium production in DT fueled fusion reactors. A core-shell type adsorbent was proposed for lithium isotope separation by chromatography. The mass transfer model in a chromatographic column consisted of 4 steps, such as convection and dispersion in the column, transfer through liquid films, intra-particle diffusion and and adsorption or desorption at the local adsorption sites. A model was developed and concentration profiles and time variation in the column were numerically simulated. It became clear that core-shell type adsorbents with thin porous shell were saturated rapidly relatively to fully porous one andmore » established a sharp edge of adsorption band. This is very important feature because lithium isotope separation requires long-distance development of adsorption band. The values of HETP (Height Equivalent of a Theoretical Plate) for core-shell adsorbent packed column were estimated by statistical moments of the step response curve. The value of HETP decreased with the thickness of the porous shell. A core-shell type adsorbent is, then, useful for lithium isotope separation. (authors)« less

Impacts of amount of impregnated iron in granular activated carbon on arsenate adsorption capacities and kinetics.

PubMed

Chang, Qigang; Lin, Wei; Ying, Wei-Chi

2012-06-01

Iron-impregnated granular activated carbons (Fe-GAC) can remove arsenic effectively from water. In this study, Fe-GACs with iron content of 1.64 to 28.90% were synthesized using a new multi-step procedure for the investigation of effects of iron amount on arsenic adsorption capacities and kinetics. Langmuir model satisfactorily fit arsenic adsorption on Fe-GACs. The maximum arsenic adsorption capacity (q(m)) increased significantly with iron impregnation and reached 1,867 to 1,912 microg/g with iron content of 9.96 to 13.59%. Further increase of iron content (> 13.59%) caused gradual decrease of q(m). It was found that the amount of impregnated iron showed little impact on the affinity for arsenate. Kinetic study showed that the amount of impregnated iron affected the arsenic intraparticle diffusion rate greatly. The pseudo-second-order kinetic model fit arsenic adsorption kinetics on Fe-GACs better than the pseudo-first-order model. The arsenic adsorption rate increased with increasing of iron content from 1.64% to 13.59%, and then decreased with more impregnated iron (13.59 to 28.90%).

The study of zinc ions binding to casein.

PubMed

Pomastowski, P; Sprynskyy, M; Buszewski, B

2014-08-01

The presented research was focused on physicochemical study of casein properties and the kinetics of zinc ions binding to the protein. Moreover, a fast and simple method of casein extraction from cow's milk has been proposed. Casein isoforms, zeta potential (ζ) and particle size of the separated caseins were characterized with the use of capillary electrophoresis, zeta potential analysis and field flow fractionation (FFF) technique, respectively. The kinetics of the metal-binding process was investigated in batch adsorption experiments. Intraparticle diffusion model, first-order and zero-order kinetic models were applied to test the kinetic experimental data. Analysis of changes in infrared bands registered for casein before and after zinc binding was also performed. The obtained results showed that the kinetic process of zinc binding to casein is not homogeneous but is expressed with an initial rapid stage with about 70% of zinc ions immobilized by casein and with a much slower second step. Maximum amount of bound zinc in the experimental conditions was 30.04mgZn/g casein. Copyright © 2014 Elsevier B.V. All rights reserved.

Biosorption of Acid Black 172 and Congo Red from aqueous solution by nonviable Penicillium YW 01: kinetic study, equilibrium isotherm and artificial neural network modeling.

PubMed

Yang, Yuyi; Wang, Guan; Wang, Bing; Li, Zeli; Jia, Xiaoming; Zhou, Qifa; Zhao, Yuhua

2011-01-01

The main objective of this work was to investigate the biosorption performance of nonviable Penicillium YW 01 biomass for removal of Acid Black 172 metal-complex dye (AB) and Congo Red (CR) in solutions. Maximum biosorption capacities of 225.38 and 411.53 mg g(-1) under initial dye concentration of 800 mg L(-1), pH 3.0 and 40 °C conditions were observed for AB and CR, respectively. Biosorption data were successfully described with Langmuir isotherm and the pseudo-second-order kinetic model. The Weber-Morris model analysis indicated that intraparticle diffusion was the limiting step for biosorption of AB and CR onto biosorbent. Analysis based on the artificial neural network and genetic algorithms hybrid model indicated that initial dye concentration and temperature appeared to be the most influential parameters for biosorption process of AB and CR onto biosorbent, respectively. Characterization of the biosorbent and possible dye-biosorbent interaction were confirmed by Fourier transform infrared spectroscopy and scanning electron microscopy. Copyright © 2010 Elsevier Ltd. All rights reserved.

Removal of basic dyes from aqueous solutions with a treated spent bleaching earth.

PubMed

Mana, Mohamed; Ouali, Mohand-Said; de Menorval, L C

2007-03-01

A spent bleaching earth from an edible oil refinery was treated by impregnation with a normal sodium hydroxide solution followed by mild thermal treatment (100 degrees C). The obtained material (TSBE) was washed, dried, and characterized by X-ray diffraction, FTIR, SEM, BET, and thermal analysis. The clay structure was not apparently affected by the treatment and the impregnated organic matter was quantitatively removed. We have investigated the comparative sorption of safranine and methylene blue on this material, the spent bleaching earth (SBE), and the virgin bleaching earth (VBE). The kinetic results fit the pseudo-second-order kinetic model and the Weber and Morris intraparticle diffusion model. The pH had no effect on the sorption efficiency. The sorption isotherms followed the Langmuir model for various sorbent concentrations with good values of the determination coefficient. A linear relationship was found between the calculated maximum removal capacity and the solid/solution ratio. A comparison between the results obtained with this material and those of the literature highlighted the low cost and the good removal capacity of treated spent bleaching earth.

Pyridinium-functionalized magnetic mesoporous silica nanoparticles as a reusable adsorbent for phosphate removal from aqueous solution.

PubMed

Ma, Fang; Du, Hongtao; Li, Ronghua; Zhang, Zengqiang

In this work, pyridinium-functionalized silica nanoparticles adsorbent (PC/SiO2/Fe3O4) was synthesized for phosphate removal from aqueous solutions. The removal efficiency of phosphate on the PC/SiO2/Fe3O4 was carried out and investigated under various conditions such as pH, contact temperature and initial concentration. The results showed that the adsorption equilibrium could be reached within 10 min, which fitted a Langmuir isotherm model, with maximum adsorption capacity of 94.16 mg/g, and the kinetic data were fitted well by pseudo-second-order and intra-particle diffusion models. Phosphate loaded on the adsorbents could be easily desorbed with 0.2 mol/L of NaOH, and the adsorbents showed good reusability. The adsorption capacity was still around 50 mg/g after 10 times of reuse. All the results demonstrated that this pyridinium-functionalized mesoporous material could be used for the phosphate removal from aqueous solution and it was easy to collect due to its magnetic properties.

Development Of ABEC Column For Separation Of Tc-99 From Northstar Dissolved Target Solution

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stepinski, Dominique C.; Bennett, Megan E.; Naik, Seema R.

Batch and column breakthrough experiments were performed to determine isotherms and mass-transfer parameters for adsorption of Tc on aqueous biphasic extraction chromatographic (ABEC) sorbent in two solutions: 200 g/L Mo, 5.1 M K +, 1 M OH -, and 0.1 M NO 3 - (Solution A) and 200 g/L Mo, 9.3 M K +, 5 M OH -, and 0.1 M NO 3 - (Solution B). Good agreement was found between the isotherm values obtained by batch and column breakthrough studies for both Solutions A and B. Potassium-pertechnetate intra-particle diffusivity on ABEC resin was estimated by VERSE simulations, and goodmore » agreement was found among a series of column-breakthrough experiments at varying flow velocities, column sizes, and technetium concentrations. However, testing of 10 cc cartridges provided by NorthStar with Solutions A and B did not give satisfactory results, as significant Tc breakthrough was observed and ABEC cartridge performance varied widely among experiments. These different experimental results are believed to be due to inconsistent preparation of the ABEC resin prior to packing and/or inconsistent packing.« less

Kevlar based nanofibrous particles as robust, effective and recyclable absorbents for water purification.

PubMed

Nie, Chuanxiong; Peng, Zihang; Yang, Ye; Cheng, Chong; Ma, Lang; Zhao, Changsheng

2016-11-15

Developing robust and recyclable absorbents for water purification is of great demand to control water pollution and to provide sustainable water resources. Herein, for the first time, we reported the fabrication of Kevlar nanofiber (KNF) based composite particles for water purification. Both the KNF and KNF-carbon nanotube composite particles can be produced in large-scale by automatic injection of casting solution into ethanol. The resulted nanofibrous particles showed high adsorption capacities towards various pollutants, including metal ions, phenylic compounds and various dyes. Meanwhile, the adsorption process towards dyes was found to fit well with the pseudo-second-order model, while the adsorption speed was controlled by intraparticle diffusion. Furthermore, the adsorption capacities of the nanofibrous particles could be easily recovered by washing with ethanol. In general, the KNF based particles integrate the advantages of easy production, robust and effective adsorption performances, as well as good recyclability, which can be used as robust absorbents to remove toxic molecules and forward the application of absorbents in water purification. Copyright © 2016 Elsevier B.V. All rights reserved.

Performance, kinetics, and equilibrium of methylene blue adsorption on biochar derived from eucalyptus saw dust modified with citric, tartaric, and acetic acids.

PubMed

Sun, Lei; Chen, Dongmei; Wan, Shungang; Yu, Zebin

2015-12-01

Biochar derived from eucalyptus saw dust modified with citric, tartaric, and acetic acids at low temperatures was utilized as adsorbent to remove methylene blue (MB) from aqueous solutions. Fourier transform infrared spectroscopy analysis showed that the carboxyl group was introduced on the biochar surface. Adsorption experiment data indicated that eucalyptus saw dust modified with citric acid showed higher MB adsorption efficiency than that modified with tartaric and acetic acids. Pseudo-second-order kinetics was the most suitable model for describing MB adsorption on biochar compared with pseudo-first-order, Elovich, and intraparticle diffusion models. The calculated values of ΔG(0) and ΔH(0) indicated the spontaneous and endothermic nature of the adsorption process. MB adsorption on biochar followed the Langmuir isotherm. The maximum adsorption capacities for eucalyptus saw dust modified with citric, tartaric, and acetic acids were 178.57, 99.01, and 29.94 mg g(-1), respectively, at 35°C. Copyright © 2015 Elsevier Ltd. All rights reserved.

Hysteresis and Phase Transitions in a Lattice Regularization of an Ill-Posed Forward-Backward Diffusion Equation

NASA Astrophysics Data System (ADS)

Helmers, Michael; Herrmann, Michael

2018-03-01

We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

NASA Astrophysics Data System (ADS)

Abramov, Rafail V.; Otto, Jasmine T.

2018-05-01

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

A Comparison of Some Difference Schemes for a Parabolic Problem of Zero-Coupon Bond Pricing

NASA Astrophysics Data System (ADS)

Chernogorova, Tatiana; Vulkov, Lubin

2009-11-01

This paper describes a comparison of some numerical methods for solving a convection-diffusion equation subjected by dynamical boundary conditions which arises in the zero-coupon bond pricing. The one-dimensional convection-diffusion equation is solved by using difference schemes with weights including standard difference schemes as the monotone Samarskii's scheme, FTCS and Crank-Nicolson methods. The schemes are free of spurious oscillations and satisfy the positivity and maximum principle as demanded for the financial and diffusive solution. Numerical results are compared with analytical solutions.

A high-order Lagrangian-decoupling method for the incompressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.

1989-01-01

A high-order Lagrangian-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) Lagrangian variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation finite-difference schemes for integration along characteristics; (3) finite element or spectral element spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous finite element characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral element spatial discretization.

The general relativistic thin disc evolution equation

NASA Astrophysics Data System (ADS)

Balbus, Steven A.

2017-11-01

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

NASA Astrophysics Data System (ADS)

Qin, Shanlin; Liu, Fawang; Turner, Ian W.

2018-03-01

The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

Evaluation of the telegrapher's equation and multiple-flux theories for calculating the transmittance and reflectance of a diffuse absorbing slab.

PubMed

Kong, Steven H; Shore, Joel D

2007-03-01

We study the propagation of light through a medium containing isotropic scattering and absorption centers. With a Monte Carlo simulation serving as the benchmark solution to the radiative transfer problem of light propagating through a turbid slab, we compare the transmission and reflection density computed from the telegrapher's equation, the diffusion equation, and multiple-flux theories such as the Kubelka-Munk and four-flux theories. Results are presented for both normally incident light and diffusely incident light. We find that we can always obtain very good results from the telegrapher's equation provided that two parameters that appear in the solution are set appropriately. We also find an interesting connection between certain solutions of the telegrapher's equation and solutions of the Kubelka-Munk and four-flux theories with a small modification to how the phenomenological parameters in those theories are traditionally related to the optical scattering and absorption coefficients of the slab. Finally, we briefly explore how well the theories can be extended to the case of anisotropic scattering by multiplying the scattering coefficient by a simple correction factor.

Conformable derivative approach to anomalous diffusion

NASA Astrophysics Data System (ADS)

Zhou, H. W.; Yang, S.; Zhang, S. Q.

2018-02-01

By using a new derivative with fractional order, referred to conformable derivative, an alternative representation of the diffusion equation is proposed to improve the modeling of anomalous diffusion. The analytical solutions of the conformable derivative model in terms of Gauss kernel and Error function are presented. The power law of the mean square displacement for the conformable diffusion model is studied invoking the time-dependent Gauss kernel. The parameters related to the conformable derivative model are determined by Levenberg-Marquardt method on the basis of the experimental data of chloride ions transportation in reinforced concrete. The data fitting results showed that the conformable derivative model agrees better with the experimental data than the normal diffusion equation. Furthermore, the potential application of the proposed conformable derivative model of water flow in low-permeability media is discussed.

Ionic channels: natural nanotubes described by the drift diffusion equations

NASA Astrophysics Data System (ADS)

Eisenberg, Bob

2000-05-01

Ionic channels are a large class of proteins with holes down their middle that control a wide range of cellular functions important in health and disease. Ionic channels can be analysed using a combination of the Poisson and drift diffusion equations familiar from computational electronics because their behavior is dominated by the electrical properties of their simple structure.

Analysis of pulse thermography using similarities between wave and diffusion propagation

NASA Astrophysics Data System (ADS)

Gershenson, M.

2017-05-01

Pulse thermography or thermal wave imaging are commonly used as nondestructive evaluation (NDE) method. While the technical aspect has evolve with time, theoretical interpretation is lagging. Interpretation is still using curved fitting on a log log scale. A new approach based directly on the governing differential equation is introduced. By using relationships between wave propagation and the diffusive propagation of thermal excitation, it is shown that one can transform from solutions in one type of propagation to the other. The method is based on the similarities between the Laplace transforms of the diffusion equation and the wave equation. For diffusive propagation we have the Laplace variable s to the first power, while for the wave propagation similar equations occur with s2. For discrete time the transformation between the domains is performed by multiplying the temperature data vector by a matrix. The transform is local. The performance of the techniques is tested on synthetic data. The application of common back projection techniques used in the processing of wave data is also demonstrated. The combined use of the transform and back projection makes it possible to improve both depth and lateral resolution of transient thermography.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

NASA Technical Reports Server (NTRS)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Extracting surface diffusion coefficients from batch adsorption measurement data: application of the classic Langmuir kinetics model.

PubMed

Chu, Khim Hoong

2017-11-09

Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 -9 to 10 -6  cm 2 /s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.

Turbo fluid machinery and diffusers

NASA Technical Reports Server (NTRS)

Sakurai, T.

1984-01-01

The general theory behind turbo devices and diffusers is explained. Problems and the state of research on basic equations of flow and experimental and measuring methods are discussed. Conventional centrifugation-type compressor and fan diffusers are considered in detail.

Patterns induced by super cross-diffusion in a predator-prey system with Michaelis-Menten type harvesting.

PubMed

Liu, Biao; Wu, Ranchao; Chen, Liping

2018-04-01

Turing instability and pattern formation in a super cross-diffusion predator-prey system with Michaelis-Menten type predator harvesting are investigated. Stability of equilibrium points is first explored with or without super cross-diffusion. It is found that cross-diffusion could induce instability of equilibria. To further derive the conditions of Turing instability, the linear stability analysis is carried out. From theoretical analysis, note that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes by means of weakly nonlinear theory. Dynamical analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, the theoretical results are illustrated via numerical simulations. Copyright © 2018. Published by Elsevier Inc.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, Harold E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 X 10 to the minus 7th power squared cm per sec + or - 30 percent in 45 percent potassium hydroxide and 1.4 x 10 to the minus 7 squared cm per sec + or - 25 percent in 40 percent sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite size chambers. Details and discussion of the experimental method are also given.

Determination of the zincate diffusion coefficient and its application to alkaline battery problems

NASA Technical Reports Server (NTRS)

May, C. E.; Kautz, H. E.

1978-01-01

The diffusion coefficient for the zincate ion at 24 C was found to be 9.9 x 10 to the -7th power sq cm/sec + or - 30% in 45% potassium hydroxide and 1.4 x 10 to the -7th power sq cm/sec + or - 25% in 40% sodium hydroxide. Comparison of these values with literature values at different potassium hydroxide concentrations show that the Stokes-Einstein equation is obeyed. The diffusion coefficient is characteristic of the zincate ion (not the cation) and independent of its concentration. Calculations with the measured value of the diffusion coefficient show that the zinc concentration in an alkaline zincate half-cell becomes uniform throughout in tens of hours by diffusion alone. Diffusion equations are derived which are applicable to finite-size chambers. Details and discussion of the experimental method are also given.

Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory.

PubMed

Contini, D; Martelli, F; Zaccanti, G

1997-07-01

The diffusion approximation of the radiative transfer equation is a model used widely to describe photon migration in highly diffusing media and is an important matter in biological tissue optics. An analysis of the time-dependent diffusion equation together with its solutions for the slab geometry and for a semi-infinite diffusing medium are reported. These solutions, presented for both the time-dependent and the continuous wave source, account for the refractive index mismatch between the turbid medium and the surrounding medium. The results have been compared with those obtained when different boundary conditions were assumed. The comparison has shown that the effect of the refractive index mismatch cannot be disregarded. This effect is particularly important for the transmittance. The discussion of results also provides an analysis of the role of the absorption coefficient in the expression of the diffusion coefficient.

Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.

PubMed

Lund, Steven P; Hubbard, Joseph B; Halter, Michael

2014-11-06

Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.

FROM THE HISTORY OF PHYSICS: Mysteries of diffusion and labyrinths of destiny

NASA Astrophysics Data System (ADS)

Bakunin, Oleg G.

2003-03-01

The role of prominent Soviet physicist B I Davydov in the development of our understanding of diffusion is briefly reviewed, with emphasis on the ideas he put forward in the 1930s: introducing additional partial derivatives into diffusion equations and extending diffusion concepts to phase space.

Some basic mathematical methods of diffusion theory. [emphasis on atmospheric applications

NASA Technical Reports Server (NTRS)

Giere, A. C.

1977-01-01

An introductory treatment of the fundamentals of diffusion theory is presented, starting with molecular diffusion and leading up to the statistical methods of turbulent diffusion. A multilayer diffusion model, designed to permit concentration and dosage calculations downwind of toxic clouds from rocket vehicles, is described. The concepts and equations of diffusion are developed on an elementary level, with emphasis on atmospheric applications.

Computation of adsorption parameters for the removal of dye from wastewater by microwave assisted sawdust: Theoretical and experimental analysis.

PubMed

S, Suganya; P, Senthil Kumar; A, Saravanan; P, Sundar Rajan; C, Ravikumar

2017-03-01

In this research, the microwave assistance has been employed for the preparation of novel material from agro/natural bio-waste i.e. sawdust, for the effective removal of methylene blue (MB) dye from aqueous solution. The characterization of the newly prepared microwave assisted sawdust (MASD) material was performed by using FTIR, SEM and XRD analyses. In order to obtain the maximum removal of MB dye from wastewater, the adsorption experimental parameters such as initial dye concentration, contact time, solution pH and adsorbent dosage were optimized by trial and error approach. The obtained experimental results were applied to the different theoretical models to predict the system behaviour. The optimum conditions for the maximum removal MB dye from aqueous solution for an initial MB dye concentration of 25mg/L was calculated as: adsorbent dose of 3g/L, contact time of 90min, solution pH of 7.0 and at the temperature of 30°C. Freundlich and pseudo-second order models was best obeyed with the studied experimental data. Langmuir maximum monolayer adsorption capacity of MASD for MB dye removal was calculated as 58.14mg of MB dye/g of MASD. Adsorption diffusion model stated that the present adsorption system was controlled by intraparticle diffusion model. The obtained results proposed that, novel MASD was considered to be an effective and low-cost adsorbent material for the removal of dye from wastewater. Copyright © 2017 Elsevier B.V. All rights reserved.

Adsorption of microcystin-LR on mesoporous carbons and its potential use in drinking water source.

PubMed

Park, Jeong-Ann; Jung, Sung-Mok; Yi, In-Geol; Choi, Jae-Woo; Kim, Song-Bae; Lee, Sang-Hyup

2017-06-01

Microcystin-LR (MC-LR) is a common toxin derived from cyanobacterial blooms an effective, rapid and non-toxic method needs to be developed for its removal from drinking water treatment plants (DWTP). For an adsorption-based method, mesoporous carbon can be a promising supplemental adsorbent. The effect of mesoporous carbon (MC1, MC2, and MC3) properties and water quality parameters on the adsorption of MC-LR were investigated and the results were analyzed by kinetic, isotherm, thermodynamic, Derjaguin-Landau-Verwey-Overbeek (DLVO), and intraparticle diffusion models. MC1 was the most appropriate type for the removal of MC-LR with a maximum adsorption capacity of 35,670.49 μg/g. Adsorption of MC-LR is a spontaneous reaction dominated by van der Waals interactions. Pore sizes of 8.5-14 nm enhance the pore diffusion of MC-LR from the surface to the mesopores of MC1. The adsorption capacity was not sensitive to changes in the pH (3.2-8.0) and the existence of organic matter (2-5 mg/L). Furthermore, the final concentration of MC-LR was below the WHO guideline level after a 10-min reaction with 20 mg/L of MC1 in the Nak-Dong River, a drinking water source. The MC-LR adsorption mainly competed with humic substances (500-1000 g/mole); however, they did not have a great effect on adsorption. Copyright © 2017. Published by Elsevier Ltd.

Equilibrium and kinetics study on hexavalent chromium adsorption onto diethylene triamine grafted glycidyl methacrylate based copolymers.

PubMed

Maksin, Danijela D; Nastasović, Aleksandra B; Milutinović-Nikolić, Aleksandra D; Suručić, Ljiljana T; Sandić, Zvjezdana P; Hercigonja, Radmila V; Onjia, Antonije E

2012-03-30

Two porous and one non-porous crosslinked poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) [abbreviated PGME] were prepared by suspension copolymerization and functionalized with diethylene triamine [abbreviated PGME-deta]. Samples were characterized by elemental analysis, mercury porosimetry, scanning electron microscopy with energy-dispersive X-ray spectroscopy, and transmission electron microscopy. Kinetics of Cr(VI) sorption by PGME-deta were investigated in batch static experiments, in the temperature range 25-70°C. Sorption was rapid, with the uptake capacity higher than 80% after 30 min. Sorption behavior and rate-controlling mechanisms were analyzed using five kinetic models (pseudo-first order, pseudo-second order, Elovich, intraparticle diffusion and Bangham model). Kinetic studies showed that Cr(VI) adsorption adhered to the pseudo-second-order model, with definite influence of pore diffusion. Equilibrium data was tested with Langmuir, Freundlich and Tempkin adsorption isotherm models. Langmuir model was the most suitable indicating homogeneous distribution of active sites on PGME-deta and monolayer sorption. The maximum adsorption capacity from the Langmuir model, Q(max), at pH 1.8 and 25°C was 143 mg g(-1) for PGME2-deta (sample with the highest amino group concentration) while at 70°C Q(max) reached the high value of 198 mg g(-1). Thermodynamic parameters revealed spontaneous and endothermic nature of Cr(VI) adsorption onto PGME-deta. Copyright © 2012 Elsevier B.V. All rights reserved.

Sorption specificity and desorption hysteresis of gibberellic acid on ferrihydrite compared to goethite, hematite, montmorillonite, and kaolinite.

PubMed

Zhang, Li; Liu, Fei; Chen, Liang

2017-08-01

The pesticide gibberellic acid (GA 3 ) is a potential endocrine disruptor and environmental toxin; therefore, research into its environmental fate is warranted. Batch studies were conducted to investigate the sorption and desorption characteristics of GA 3 on aquifer media. The results demonstrated special sorption characteristic of GA 3 on ferrihydrite compared to goethite, hematite, montmorillonite, and kaolinite, where the sorption kinetics of GA 3 on ferrihydrite was fitted well with the pseudo-second-order, Elovich, and intra-particle diffusion models. The sorption kinetics of GA 3 on ferrihydrite indicated an initial high sorption rate followed by a slow reaction process. The initial high GA 3 sorption rate may be related to electrostatic sorption and surface complexation reactions on the outer surfaces and at the macropore entrances of ferrihydrite. While the slow step was controlled by GA 3 diffusion into mesopore of ferrihydrite. Analysis of the desorption hysteresis indicated a high hysteresis index (HI) ranging from 0.68 to 17.32, and a low desorption percentage ranging from 18 to 48%. After sufficient desorption, the calculated maximum residual GA 3 quantity due to surface complexation reactions with the ferrihydrite coordinated unsaturated sites was 9.05 ± 0.12 mg g -1 . The calculated maximum quantity of GA 3 trapped within the mesopore was 16.23 ± 0.91 mg g -1 . Graphical Abstract Schematic overview of GA 3 sorption and desorption on five minerals in groundwater.

Assessment of the use of Moringa oleifera seed husks for removal of pesticide diuron from contaminated water.

PubMed

Bezerra, Charleston de O; Cusioli, Luís F; Quesada, Heloise B; Nishi, Letícia; Mantovani, Daniel; Vieira, Marcelo F; Bergamasco, Rosangela

2018-06-22

Considering the need of new technologies for the removal of pesticides from the aqueous environment, the Moringa oleifera seed husks (h-MO) was investigated for the diuron adsorption from contaminated water at different temperatures and solute concentrations. The biosorbent used in this study was characterized by chemical, structural and textural analyzes. The best experimental condition for the biosorption was determined by evaluating the mass of the biosorbent and the pH solution. It was found a good adsorption capacity for the herbicide where the maximum adsorption capacity was 14.74 mg/g at pH 5 and 45°C. In addition, the adsorption process of diuron by the h-MO occurred spontaneously, in which, ΔG° values increased as the temperature increased meaning that the process tends to a more energetically favorable process at higher temperatures. Both Langmuir and Sips isotherm models presented satisfactory adjustment at all temperatures and the pseudo-second-order model presented the best fit for the experimental results. The application of the intra-particle diffusion model showed that the adsorption process started instantaneously through the boundary layer of the adsorbent and that the pore diffusion step was a limiting step in the process. Finally, the capacity of the h-MO was compared with others adsorbents that had been used to diuron removal from contaminated where it was found that the adsorption capacity of the h-MO is much higher than other natural adsorbents.

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

NASA Astrophysics Data System (ADS)

Saurel, Richard; Pantano, Carlos

2018-01-01

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid-governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. More sophisticated materials than fluids (e.g., elastic-plastic materials) have been considered as well.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Numerical simulation of double‐diffusive finger convection

USGS Publications Warehouse

Hughes, Joseph D.; Sanford, Ward E.; Vacher, H. Leonard

2005-01-01

A hybrid finite element, integrated finite difference numerical model is developed for the simulation of double‐diffusive and multicomponent flow in two and three dimensions. The model is based on a multidimensional, density‐dependent, saturated‐unsaturated transport model (SUTRA), which uses one governing equation for fluid flow and another for solute transport. The solute‐transport equation is applied sequentially to each simulated species. Density coupling of the flow and solute‐transport equations is accounted for and handled using a sequential implicit Picard iterative scheme. High‐resolution data from a double‐diffusive Hele‐Shaw experiment, initially in a density‐stable configuration, is used to verify the numerical model. The temporal and spatial evolution of simulated double‐diffusive convection is in good agreement with experimental results. Numerical results are very sensitive to discretization and correspond closest to experimental results when element sizes adequately define the spatial resolution of observed fingering. Numerical results also indicate that differences in the molecular diffusivity of sodium chloride and the dye used to visualize experimental sodium chloride concentrations are significant and cause inaccurate mapping of sodium chloride concentrations by the dye, especially at late times. As a result of reduced diffusion, simulated dye fingers are better defined than simulated sodium chloride fingers and exhibit more vertical mass transfer.

New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.

PubMed

Ingo, Carson; Magin, Richard L; Parrish, Todd B

2014-11-01

Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.